Question 1

Which of the following best describes a function $$f as $$defined in calculus?

Accepted Answer

A rule that assigns to each value $$x in a $$set $$D a $$unique value $$f(x).$$

Question 2

Given the diagram of a function machine, what is the domain and range in the context of the function $$f$$?

Accepted Answer

Domain: all possible input values $$x$$; Range: all possible output values $$f(x).$$

Question 3

Which graph passes the vertical line test and therefore represents a function?

Accepted Answer

A parabola opening upwards.

Question 4

What does the vertical line test determine?

Accepted Answer

Whether a graph represents a function by checking if any vertical line intersects the graph more than once.

Question 5

For the function $$f(x) = x^2$ + 1$$, what are the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$[1, \infty)$$

Question 6

Consider the function $$z = \sqrt{4 - t^2$}. $$What is the domain of this function?

Accepted Answer

$$-2 \leq t \leq 2$$

Question 7

Given $$w = \frac{1}{u-1}$$, which value is excluded from the domain?

Accepted Answer

$$u = 1$$

Question 8

A stone is thrown vertically upward with $$h(t) = 30t - 5t^2$. What is the appropriate domain for t$ in this context?

Accepted Answer

$$0 \leq t \leq 6$$

Question 9

Which of the following is the correct definition of a composite function $$f \circ g$$?

Accepted Answer

$$(f \circ g)(x) = f(g(x))$$

Question 10

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

Accepted Answer

$$f(g(x)) = (x^2$)^2 + 1$$ = $$x^4 + 1$

Question 11

Which of the following best describes the slope of the secant line between points $$P(x, f(x))$$ and $$Q(x+h, f(x+h)) on $$the graph of $$y = f(x)$$?

Accepted Answer

$$m_{sec} = \frac{f(x+h) - f(x)}{h}$$

Question 12

If a graph is symmetric with respect to the y-axis, which property must its function $$f$$ satisfy?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain

Question 13

Which of the following is an odd function?

Accepted Answer

$$f(x) = x^3$ - x$$

Question 14

Which of the following is true about the range of $$f(x) = x^n$$ where $$n is a $$positive even integer?

Accepted Answer

The range is all nonnegative real numbers.

Question 15

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 16

Which transformation produces the graph of $$y = f(x) + d$$ from $$y = f(x)$$?

Accepted Answer

A vertical shift by $$d$$ units (up if $$d \u003e 0$$, down if $$d \u003c 0)$$

Question 17

Which of the following is the correct domain for the rational function $$f(x) = \frac{3x^3$ - x - 1}{x^3$ + 2x^2$ - 6}$$?

Accepted Answer

All real numbers except where $$x^3$$ + $$2x^2 - 6 = 0$

1.1 & 1.2

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