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9/22/2020

1.

HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.1.004.

PRACTICE ANOTHER

The graphs of f and g are given.

(a) State the values of f(2) and g(3). f(2) = 2

2

g(3) = 4

4

(b) For what values of x is f(x) = g(x)? (Enter your answers as a comma-separated list.) x= $$−2,2

(c) Estimate the solutions of the equation f(x) = −1. (Enter your answers as a comma-separated list.) x= $$−3,4

(d) On what interval is f decreasing? (Enter your answer using interval notation.) $$[0,4]

(e) State the domain and range of f. (Enter your answers in interval notation.) $$[−4,4] domain

$$[−2,3] range

(f) State the domain and range of g. (Enter your answers in interval notation.) $$[−4,3] domain

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign range

$$[2.5,4]

Solution or Explanation Click to View Solution Enhanced Feedback Please try again. For finding function values on a graph, remember to first locate the vertical line corresponding to the given x-value, then locate the y-value of the point at which it intersects the function. For finding all x-values that correspond to a given function value, remember to first locate the horizontal line corresponding to the given function value, then locate the x-values of any points at which it intersects the function. For finding the interval on which f is decreasing, remember that f is decreasing if f(x1) > f(x2) for any x1, x2 such that x1 < x2 on the interval. The domain of a function is the set of inputs on which the function is defined, whereas the range is the set of all outputs.

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.1.009.

MY NOTES

ASK YOUR TEACHER

Consider the following graph.

Determine whether the curve is the graph of a function of x. Yes, it is a function. No, it is not a function.

If it is, state the domain and range of the function. (Enter your answers using interval notation. If it is not a function, enter DNE in all blanks.) $$[−3,−2]∪[−2,2] domain

$$[−3,−2]∪[−1,3] range

Solution or Explanation Click to View Solution Enhanced Feedback Please try again. Remember, a function is a rule that assigns to each element x in the domain exactly one element, called f(x), in the range. The graph of f is the set of points (x, y) in the plane such that y = f(x).

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.1.025.

PRACTICE ANOTHER

If f(x) = 3x2 − x + 3, find the following. f(3) = 27

27

f(−3) = 33

33

$$3a2−a+3 f (a ) =

$$3a2+a+3 f(−a) =

$$3a2+5a+5 f(a + 1) =

$$6a2−2a+6 2f(a) =

$$12a2−2a+3 f(2a) =

$$3a4−a2+3 f (a 2 ) =

$$6a2−2a+6 [f(a)]2 =

$$3a2+6ah+3h2−a−h+3 f (a + h ) =

Solution or Explanation Click to View Solution Enhanced Feedback Please try again. To evaluate f for a specific term, replace each x by that term in the expression for f(x). To ensure correct simplification, start by surrounding each instance of the term with parentheses.

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.1.027.

PRACTICE ANOTHER

Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 4 + 4x − x2,

f(4 + h) − f(4) h

$$−h−2x+4.

Solution or Explanation Click to View Solution Enhanced Feedback Please try again. To evaluate f(a + h), replace x by (a + h) in the expression for f(x). Substitute this into the given expression and simplify.

5.

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SCALC8 1.1.030.

PRACTICE ANOTHER

Evaluate the difference quotient for the given function. Simplify your answer. f(x) =

x+7 , x+3

f(x) − f(1) x−1

$$−1h+4

Solution or Explanation Click to View Solution

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.1.051.

PRACTICE ANOTHER

Find an expression for the function whose graph is the given curve. (Assume that the points are in the form (x, f(x)).) The line segment joining the points (3, −2), and (7, 8) f(x) = $$(x+3)(x+7)

Find the domain of the function. (Enter your answer using interval notation.) $$(−∞,∞)

Solution or Explanation Click to View Solution

7.

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SCALC8 1.1.061.

PRACTICE ANOTHER

Find a formula for the described function. An open rectangular box with volume 4 m3 has a square base. Express the surface area SA of the box as a function of the length of a side of the base, x. SA = $$x2+(16x)

m2 State the domain of SA. (Enter your answer in interval notation.) $$(0,∞)

Solution or Explanation Click to View Solution

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.1.063.

PRACTICE ANOTHER

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. V(x) = $$4x3−64x2+240x

Solution or Explanation Click to View Solution

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.1.513.XP.MI.

PRACTICE ANOTHER

Find the domain of the function. (Enter your answer in interval notation.) g(x) =

x − 17

$$(17,∞)

Sketch the graph of the function.

Solution or Explanation Click to View Solution

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.3.002.

PRACTICE ANOTHER

Explain how each graph is obtained from the graph of y = f(x). (a)

y = f(x) + 3 Shift the graph 3 units to the left. Shift the graph 3 units to the right. Stretch the graph horizontally and vertically by a factor of 3. Shift the graph 3 units upward. Shift the graph 3 units downward.

(b)

y = f (x + 3 ) Shift the graph 3 units to the right. Shift the graph 3 units to the left. Shift the graph 3 units downward. Shift the graph 3 units upward. Stretch the graph horizontally and vertically by a factor of 3.

(c)

y = 3f(x) Stretch the graph vertically by a factor of 3. Shift the graph 3 units upward. Shift the graph 3 units to the left. Stretch the graph horizontally and vertically by a factor of 3. Shrink the graph horizontally by a factor of 3.

(d)

y = f(3x) Shrink the graph horizontally by a factor of 3. Shift the graph 3 units upward. Stretch the graph horizontally and vertically by a factor of 3. Stretch the graph vertically by a factor of 3. Shift the graph 3 units to the left.

(e)

y = −f(x) − 1

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign First reflect the graph about the x-axis, and then shift it 1 unit left. First reflect the graph about the x-axis, and then shift it 1 unit upward. First reflect the graph about the y-axis, and then shift it 1 unit upward. First reflect the graph about the x-axis, and then shift it 1 unit downward. First reflect the graph about the y-axis, and then shift it 1 unit downward.

(f)

y = 3f

1 x 3

Shrink the graph horizontally by a factor of 3. Shrink the graph horizontally and vertically by a factor of 3. Stretch the graph horizontally and vertically by a factor of 3. Stretch the graph vertically by a factor of 3. Stretch the graph horizontally by a factor of 3.

Solution or Explanation (a) To obtain the graph of y = f(x) + 3 from the graph of y = f(x), shift the graph 3 units upward. (b) To obtain the graph of y = f(x + 3) from the graph of y = f(x), shift the graph 3 units to the left. (c) To obtain the graph of y = 3f(x) from the graph of y = f(x), stretch the graph vertically by a factor of 3. (d) To obtain the graph of y = f(3x) from the graph of y = f(x), shrink the graph horizontally by a factor of 3. (e) To obtain the graph of y = −f(x) − 1 from the graph of y = f(x), first reflect the graph about the x-axis, and then shift it 1 unit downward.

(f) To obtain the graph of y = 3f

1 x 3

from the graph of y = f(x), stretch the graph horizontally and vertically by a factor of 3.

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.3.003.

MY NOTES

ASK YOUR TEACHER

The graph of y = f(x) is given. Match each equation with its graph.

(a)

y = f(x − 4) 1 2 3 4 5

(b)

y = f(x) + 3 1 2 3 4 5

(c)

y=

1 f(x) 3

1 2 3 4 5

(d)

y = −f(x + 4)

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign 1 2 3 4 5

y = 2f(x + 6)

(e) 1

2 3 4 5

Solution or Explanation Click to View Solution

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.3.015.

PRACTICE ANOTHER

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = x2 − 4x + 8

Solution or Explanation y = x2 − 4x + 8 = (x2 − 4x + 4) + 4 = (x − 2)2 + 4: Start with the graph of y = x2, shift 2 units to the right, and then shift upward 4 units.

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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SCALC8 1.3.031.

PRACTICE ANOTHER

Find each of the following functions and state their domains. (Enter the domains in interval notation.) f(x) = x3 + 5x2, (a)

g(x) = 7x2 − 3

f+g $$x3+12x2−3

f+g=

$$(−∞,∞) domain

(b)

f−g $$x3−2x2+3

f−g=

$$(−∞,∞) domain

(c)

fg $$7x5+35x4−3x3−15x2 fg =

$$(−∞,∞) domain

(d)

f /g $$x3+5x27x2−3 f/g =

$$(−√37,√37)

domain

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

Solution or Explanation Click to View Solution

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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MY NOTES

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SCALC8 1.3.037.

PRACTICE ANOTHER

Find the functions and their domains. (Enter the domains in interval notation.) f(x) = x + (a)

(f

1 , x

∘g

f

g(x) =

x + 17 x+2

$$(2x2+38x+293)x2+19x+34

∘ g)(x) = $$(0,∞)

domain

(b)

g

∘f $$(x2+17x+1)(x2+2x+1)

∘ f)(x) =

(g

$$(0,∞) domain

(c)

(f

f

∘f

$$(18x2+87x+102)3x2+27x+42

∘ f)(x) = $$(0,∞)

domain

(d)

g

∘g $$(x2+17x+1)x2+2x+1

(g

∘ g)(x) = $$(0,∞)

domain

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

Solution or Explanation Click to View Solution

15.

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SCALC8 1.3.053.

MY NOTES

ASK YOUR TEACHER

Use the given graphs of f and g to evaluate each expression, or if the expression is undefined, enter UNDEFINED.

(a)

f(g(2))

4 (b)

4 g(f(0))

2

3

∘ g)(0)

(c) -2

(f

(d)

(g

0

2 (e)

UNDEFINED

(g

-1 (f) -2

∘ f)(6)

∘ g)(−2) 4

(f

∘ f)(4)

-2

Solution or Explanation Click to View Solution Enhanced Feedback Please try again. Remember that given two functions f and g, the composite function f

∘g

is defined by (f

∘ g)(x) = f(g(x)).

To

evaluate f(g(x)) using the graph, first find g(x) using the graph. Then, using g(x) as the input, find the corresponding function value of f from the graph.

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

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WEBASSIGNCRA1 8.1.001.

PRACTICE ANOTHER

Let f(x) = 6 − 2−x + 1.

Part 1 - Graph

Graph y = f(x).

Part 2 - Domain and range

From your graph in part 1, state the domain and range of f. (Enter your answers using interval notation.) $$(−∞,∞) domain

$$(−∞,∞) range

Part 3 - One-to-one

From your graph in part 1, explain why f is one-to-one. Since y = f(x)

passes the Vertical Line Test, f is one-to-one.

Since y = f(x)

does not pass the Horizontal Line Test, f is one-to-one.

Since y = f(x)

does not pass the Vertical Line Test, f is one-to-one.

Since y = f(x)

passes the Horizontal Line Test, f is one-to-one.

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign Part 4 - f −1(x)

Find a formula for f −1(x). $$log2(−x2+1) f −1(x) =

Part 5 - Function composition

Check your answer to part 4 using function composition. (f −1 (f

∘ f)(x) =

(No Response)

∘ f −1)(x) =

(No Response)

Additional Materials

Watching

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HW # 0 Fall 20 - MATH 151, section 11, Fall 2020 | WebAssign

[–/0.43 Points]

MY NOTES

DETAILS

WEBASSIGNCRA1 8.1.007.TUT.

ASK YOUR TEACHER

PRACTICE ANOTHER

Find the x- and y-intercepts of the exponential function below. x-intercept

(x, y) =

(No Response)

y-intercept

(x, y) =

(No Response)

Solution or Explanation Part 1 of 1

Use the graph to see where the function crosses the x- and y-axes. In the graph below, the x- and y-intercepts are indicated with points.

Recall that the x-intercept is the point (a, 0) where the graph crosses the x-axis. Look at the graph and find the value of x when the graph crosses the x-axis. The graph crosses the x-axis at what value? x=1 Therefore, the x-intercept is located at the following point.

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