$$f(-x) = -f(x)$$ \text{ for all } x$

Question 1

Which of the following best describes a function $$f$$ that is increasing on an interval $$I$$?

Accepted Answer

For all $$a \u003c b in$$ $$I$$, $$f(a) \u003c f(b).$$

Question 2

Given the piecewise function $$f(x) = \begin{cases} -3, & x \leq 0 \ -3 + x^2$, & 0  2 \end{cases}$$, what is $$f(1)$$?

Accepted Answer

$$-2$$

Question 3

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

Accepted Answer

$$x^2 - x + 5$

Question 4

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

Accepted Answer

$$y = f(x) + 3$$

Question 5

Given $$f(x) = x^2$ and g(x) = 3x - 1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(3x - 1)^2$

Question 6

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 7

If $$y$$ varies directly as $$x$$ and $$y = 42$$ when $$x = 3$$, what is the equation relating $$y$$ and $$x$$?

Accepted Answer

$$y = 14x$$

Question 8

Which of the following describes a vertical stretch of the graph $$y = f(x) by a $$factor of 4?

Accepted Answer

$$y = 4f(x)$$

Question 9

If $$f(x) = x^2$ + 2x - 3$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h + 2$$

Question 10

Which of the following is the domain of $$f(x) = \sqrt{2x + 3}$$?

Accepted Answer

$$x \geq -\frac{3}{2}$$

Question 11

If $$y$$ varies inversely as $$x$$ and $$y = 22$$ when $$x = 0.4$$, what is the variation constant $$k$$?

Accepted Answer

$$8.8$$

Question 12

Which of the following graphs is symmetric with respect to the y-axis?

Accepted Answer

$$y = x^2$

Question 13

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

Accepted Answer

$$x^2 + x + 2$

Question 14

Which transformation reflects the graph of $$y = f(x)$$ across the x-axis?

Accepted Answer

$$y = -f(x)$$

Question 15

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

Accepted Answer

$$(2x + 1)^2$

Question 16

Which of the following best describes an odd function?

Accepted Answer

$$f(-x) = -f(x)$$ 	ext{ for all } x$

Question 17

Which of the following is the result of horizontally stretching the graph of $$y = x^3$ - x by a $$factor of $$\frac{1}{2}$$?

Accepted Answer

$$y = \left(\frac{1}{2}x\$$right)^3$$ - \left(\frac{1}{2}x\right)$$

Question 18

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

Accepted Answer

$$x 
eq -1$$

Question 19

Which of the following is a correct decomposition of $$h(x) = (3x - 1)^4$ as a composition of two functions f$ and g$?

Accepted Answer

$$f(x) = x^4$,\ g(x) = 3x - 1$$

College Algebra: More on Functions (Chapter 2) – Study Notes

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