Midterm (MTH 111) -2 PDF

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Quick piece of statistics take home midterm. I received full credit for this....

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1) (4 points) Which of the following (a – f) are functions? Circle your answer(s).

a)

b)

c) {(1, 8), (2, 6), (3, 8), (4, 6), (5, 8)}

d) {(1, 5), (2, 7), (1, 8), (3, 9), (4, 4)}

e) y2 = x – 3

f) x5 = 3 – y

2) (6 points) For the function 𝑓(𝑥) = a) f(–2)

b) f(x + 3)

c) f(–x)

   , 

find the following:

3) (4 points) The function f is shown on this coordinate grid.

a) What are the domain and range of f?

b) What are the x- and y-intercepts of f?

4) (6 points) The graph of the function f is shown on the coordinate grid.

a) On what interval(s) is f increasing?

b) On what interval(s) is f decreasing?

c) Is f even, odd, or neither?

5) (4 points) The function f is graphed on this coordinate grid.

a) What are the absolute maximum and absolute minimum, if they exist?

b) What are the local maximums and local minimums, if they exist?

6) (6 points) For the function 𝑓(𝑥) = 

−2𝑥 + 1 𝑖𝑓 𝑥 < 0 , sketch the graph of f. 𝑥−3 𝑖𝑓 𝑥 ≥ 0

7) (12 points) The function f is graphed on the coordinate grids. 

a. Graph 𝑔(𝑥) = 𝑓(𝑥 + 3). 

b. Graph h(x) = f(2x) – 2

8) (6 points) For the functions 𝑓(𝑥) = a) 𝑓 ∘ 𝑔

 



and 𝑔(𝑥) = , find the composite. 

b) 𝑓 ∘ 𝑓

9) (4 points) Determine if the function is one-to-one a) {(2, 6), (–3, 6), (4, 9), (1, 10)} b) {(–2, 5), (–1, 3), (3, 7), (4, 12)}

c)

d)

10) (6 points) Find the inverse of the function a) {(–2, 2), (–1, 6), (0, 8), (1, –3), (2, 9)}

b) 𝑓(𝑥) = 1 − 3𝑥

c)

𝑔(𝑥) =

 

11) (15 points) Sketch a graph of 𝑓(𝑥) = (𝑥 − 2) (𝑥 + 2)(𝑥 + 4). Determine the zeros, intercepts, multiplicities, and end behavior of the graph.

12) (15 points) Create an equation, in standard form, for the polynomial graphed here....