Question 1

Kiara and Matias drive away from a hospital at right angles to each other, with Kiara traveling at 35 mph and Matias at 40 mph. Which of the following correctly expresses the distance between them as a function of time $$t in $$hours?

Accepted Answer

$$d(t) = \sqrt{(35t)^2$ + (40t)^2$}$$

Question 2

Given the function $$f(x) = \sqrt{x + 3}$$, what is the domain of $$f$$?

Accepted Answer

$$[-3, \infty)$$

Question 3

Which transformation has been applied to the basic squaring function $$f(x) = x^2$ to obtain f(x) = 3$$ - $$x^2$$?

Accepted Answer

Reflected across the x-axis and shifted up 3 units

Question 4

Consider the piecewise function $$g(x) = \frac{1}{3}x + 3$$ for $$x \u003c 3$$ and $$g(x) = -x$$ for $$x \geq 3. $$What is $$g(4)$$?

Accepted Answer

$$g(4) = -4$$

Question 5

Given the function $$f(x) = 4$$ for $$x \leq 0$$, $$f(x) = 4 - x^2$ for 0  2$, what is f(1$$)$$?

Accepted Answer

$$f(1) = 4 - (1)^2$ = 3$$

Question 6

The graph shown is the greatest integer function $$f(x) = \lfloor x \rfloor. $$What is the range of this function?

Accepted Answer

$$\{x \mid x \in \mathbb{Z}\}$$

Question 7

Which of the following is a zero of the function $$f(x) = x^2$ - x - 2$$?

Accepted Answer

$$x = 2$$

Question 8

For the function $$f(x) = |x + 3|$$, what is the $$x-$$intercept?

Accepted Answer

$$x = -3$$

Question 9

Given $$f(x) = x^2$ + 2x + 3$$, which transformation has been applied to the basic function $$f(x) = x^2$?

Accepted Answer

Shifted left 2 units and up 3 units

Question 10

Which of the following intervals describes where the function in the graph with points $$(-1, -2)$$, $$(3, -2)$$, and $$(5, 2) is $$constant?

Accepted Answer

$$(-1, 3)$$

Question 11

Given $$f(x) = x^2$ - x - 2$$, on which intervals is the function increasing?

Accepted Answer

$$(\frac{1}{2}, \infty)$$

Question 12

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

Accepted Answer

$$(x + 2)^2$

Question 13

Which of the following is true about the symmetry of $$y = x^2$ + 2x + 3$$?

Accepted Answer

It is not symmetric with respect to the y-axis or the origin

Question 14

Given $$f(x) = x^3$ and g(x) = x - 2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(x - 2)^3$

Question 15

Which of the following describes the transformation from $$f(x) = \sqrt{x} to$$ $$g(x) = \sqrt{x + 2}$$?

Accepted Answer

Shifted left 2 units

Question 16

If $$f(x) = x^2$ and g(x) = 2x$, what is the effect of f(g(x$$))$$ compared to f(x$$)$$?

Accepted Answer

Horizontal shrink by a factor of 2

Question 17

Which of the following is the correct algebraic test for even functions?

Accepted Answer

$$f(-x) = f(x)$$

Question 18

Given $$f(x) = x^2$ - x - 2$$, what are the zeros of $$f$$?

Accepted Answer

$$x = -1$$ and $$x = 2$$

Question 19

If $$f(x) = x^2$ and g(x) = x + 3$, what is the domain of f(g(x$$))$$?

Accepted Answer

$$(-\infty, \infty)$$

Types of Functions and Their Properties: College Algebra Study Notes

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