Question 1

Given $$f(x) = 3x^2$ and g(x$$) = \frac{1}{2}x + \frac{3}{2}$$, what is g(f(3$$))$$?

Accepted Answer

$$g(f(3)) = 15.5$$

Question 2

Which of the following best describes a piecewise function?

Accepted Answer

A function defined on distinct subsets of the domain, each with its own formula

Question 3

What is the $$y-$$intercept of the piecewise function $$f(x) = \begin{cases} 4 - x^2$ & x 
eq 0 \ 3 & x = 0 \end{cases}$$?

Accepted Answer

$$3$$

Question 4

Suppose $$h(x) = |x|. $$Which of the following is true about $$h(x)$$?

Accepted Answer

$$h(x) is a $$piecewise function

Question 5

If $$f(x) = x + 2$$ and $$g(x) = 2x$$, what is $$(g \circ f)(1)$$?

Accepted Answer

$$g(f(1)) = 6$$

Question 6

A tax bracket function is defined as $$T(x) = \begin{cases} 0.1x & 0 \leq x \leq 10000 \ 1000 + 0.2(x-10000) & x \u003e 10000 \end{cases}. $$What is $$T(15000)$$?

Accepted Answer

$$T(15000) = 2000$$

Question 7

Which transformation shifts the graph of $$f(x) up by 3 $$units?

Accepted Answer

$$f(x) + 3$$

Question 8

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of (g$$ \circ f)(x)$$?

Accepted Answer

All real numbers

Question 9

Which of the following is the correct composition $$f(g(x)) if$$ $$f(x) = 2x$$ and $$g(x) = x - 1$$?

Accepted Answer

$$2(x - 1)$$

Question 10

A function $$f(x) is $$defined as $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}. $$What is $$f(-2) + f(2)$$?

Accepted Answer

$$f(-2) + f(2) = 8$$

Question 11

Which of the following is NOT a transformation of $$f(x)$$?

Accepted Answer

$$f(x) \cdot f(x)$$

Question 12

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (g$$ \circ f)(x)$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 13

Which of the following is the correct graph for $$f(x) = |x|$$?

Accepted Answer

A V-shaped graph opening upwards

Question 14

If $$f(x) = x^2$ and g(x) = 2x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 25$$

Functions: Composition, Piecewise Definitions, and Transformations

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