3.1, 3.2 notes 1105 - Functions and graphs of functions PDF

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Functions and graphs of functions...

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3.1 Functions Finding Function Values Function: No repeating x-values One-to-One functions: one x goes to exactly one y. No repeating x- values, or y-values Domain: All the x-values Range: All the y-values Example 1: For the function f defined by , evaluate a) f(3) b) f(x) + ) c) 3f(x) d) f(-x) e) -f(x) f) f(x+3)

Finding the Domain of a Function. - If there is no fraction with a variable in the denominator or radical the domain is all real numbers. - If the equation has a fraction with a variable in the denominator, set the denominator equal to zero and solve. We do this because we cannot have 0 in th denominator. - If the equation is just a radical or a fraction with a radical in the denominator, set the radicand (inside) greater than or equal to zero. We do this becaus cannot have negative numbers inside the radical. - If you have an equation with a fraction having a radical on top and a variable in the denominator, set the radicand greater than or equal to zero AND set denominator equal to zero. Example 2: Find the domain of each of the following: a)

b)

c)

d)

Form the Sum, Difference, Product, and Quotient of Two Functions

Example 3:

Difference Quotient

Example 4:

Example 5 For the functions given complete parts a-h

Example 5 For the functions given complete parts a-h

a) (f + g) (x)

b) (f - g) (x)

c)

d)

3.2 The graph of a Function Use the vertical line test. Example 1: Which graphs are graphs of a function?

Obtain Information From a Graph. Example 2:

a) Find F(-35) and f(-15)

g) What is the domain of f?

b) Find f(30) and f(0)

h) What is the range of f?

c) Is f (10) positive or negative?

i) What are the x-intercepts?

d) Is f(-35) positive or negative?

j) What are the y-intercepts?

e) For what value(s) of x is f(x)=0

k) How often does the line y=1 intersect the graph?

f) For what values of x is f(x)>0?

l) For what value(s) of x does f(x)=15?

Example 3 Determine whether the graph is that is of a function by using the vertical line test. a) What is the domain and range?

Example 3 Determine whether the graph is that is of a function by using the vertical line test. a) What is the domain and range? b) What are the intercepts? c) Find any symmetry.

Example 4:

a) b) c) d) e) f)

Is the point (-1, 2) on the graph of F? If x=4, what is f(x)? What point is on the graph of F? If f(x)=2, what is x? What point(s) are on the graph of f? What is the domain of f? List the x-intercepts, if any? List the y-intercepts, if any?...