Q: Which of the following is a piecewise function?

$$f(x) = \begin{cases} x^2$, & x \u003c 0 \\ x+1, & x \geq 0 \end{cases}$$

Question 1

Which of the following graphs does NOT represent a function?

Accepted Answer

A graph where a vertical line crosses the curve at two points.

Question 2

Given $$f(x) = x^4$ - 3$$, determine whether $$f(x) is $$even, odd, or neither.

Accepted Answer

Even, because $$f(-x) = f(x).$$

Question 3

Which transformation results in the graph of $$f(x)$$ being shifted 3 units to the left?

Accepted Answer

$$f(x+3)$$

Question 4

If $$f(x) = |x-2| + 3$$, what is the vertex of the graph?

Accepted Answer

$$(2, 3)$$

Question 5

A cost function for producing $$x$$ bicycles is $$C(x) = 200x + 5000. If $$the revenue function is $$R(x) = 350x$$, at what value of $$x$$ does the company break even?

Accepted Answer

$$x = 33.33$$

Question 6

Which of the following functions is symmetric about the origin?

Accepted Answer

$$f(x) = x^3$

Question 7

Given $$f(x) = x^2$ - 4$$, find the $$x-$$intercepts.

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 8

For the quadratic function $$f(x) = 2x^2$ - 8x + 6$$, what is the vertex?

Accepted Answer

$$(2, -2)$$

Question 9

Which of the following describes a vertical stretch of the function $$f(x) by a $$factor of 3?

Accepted Answer

$$3f(x)$$

Question 10

A population grows from 0.32g at $$t=3$$ hours to 0.51g at $$t=5$$ hours. What is the average rate of growth?

Accepted Answer

$$0.095 g/hr$$

Question 11

Which of the following is the correct formula for the average rate of change of $$f(x)$$ from $$x=a to$$ $$x=b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 12

If $$f(x) is $$increasing on $$(0, 3)$$ and decreasing on $$(-\infty, 0)$$, which of the following is true?

Accepted Answer

The function has a local minimum at $$x=0.$$

Question 13

Which of the following is a piecewise function?

Accepted Answer

$$f(x) = \begin{cases} x^2$, & x \u003c 0 \ x+1, & x \geq 0 \end{cases}$$

Question 14

Given $$f(x) = (x+3)^2$ + 2$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, 2)$$

Question 15

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(x+2)^2 - 4$

Question 16

Which of the following statements about the function $$f(x) = |x| is $$true?

Accepted Answer

It is even and symmetric about the $$y-$$axis.

Question 17

A secant line passes through the points $$(1, 3)$$ and $$(5, 11) on a $$curve. What is the slope of the secant line?

Accepted Answer

$$2$$

Question 18

If $$f(x) = x^3$ - 2x$$, on which intervals is $$f(x)$$ increasing?

Accepted Answer

$$(-\infty, -1) \cup (1, \infty)$$

Question 19

Which of the following describes a reflection of $$f(x)$$ across the $$x-$$axis?

Accepted Answer

$$-f(x)$$

Question 20

If $$f(x) = x^2$ - 4x + 7$$, complete the square to write $$f(x) in $$vertex form.

Accepted Answer

$$(x-2)^2 + 3$

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