Question 1

Which of the following functions is quadratic, and what is the nature of its vertex?

$$y = -x^2$ - 4x - 8$$

Accepted Answer

It is quadratic, concave down, and the vertex is a maximum.

Question 2

What are the coordinates of the vertex for the function $$y = (x - 5)^2$ + 1$$?

Accepted Answer

$$(5, 1)$$

Question 3

Find the x-intercepts of the function $$f(x) = 2x^2$ + x - 6.$$

Accepted Answer

$$x = -1.5, x = 2$$

Question 4

Solve the equation $$x^{1/4} = 2$ and check for extraneous solutions.

Accepted Answer

$$x = 16$$

Question 5

Given the piecewise function $$f(x) = \begin{cases} 3 & x \leq 0 \ 7 & x \u003e 0 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 3$$

Question 6

Solve the equation $$|x - \frac{1}{2}| = 5.$$

Accepted Answer

$$x = 5.5 or$$ $$x = -4.5$$

Question 7

Find the equation of the quadratic function whose graph passes through the points $$(0, 5)$$, $$(2, 9)$$, and $$(1, 12).$$

Accepted Answer

Question 8

Describe the transformation used to obtain the graph of $$g(x) = \sqrt{x} + 4$$ from $$f(x) = \sqrt{x}.$$

Accepted Answer

Shift the graph up 4 units.

Question 9

Suppose the graph of $$f(x) = x^2$ is shifted down 4 units and to the left 1 unit. What is the equation of the new graph?

Accepted Answer

$$y = (x + 1)^2$ - 4$$

Question 10

Evaluate $$(f + g)(-1)$$ for $$f(x) = x^2$ - 5x$$ and $$g(x) = 8 - x^3$.

Accepted Answer

Question 11

Find the inverse of $$g(x) = 2x + 5.$$

Accepted Answer

$$g^{-1}(x$$) = \frac{x - 5}{2}$$

Question 12

A medical researcher models the spread of a virus with the quadratic function $$y = -3x^2$ + 12x + 5$$, where $$y is $$the number of cases and $$x is $$days since outbreak. What is the maximum number of cases, and on which day does it occur?

Accepted Answer

Maximum at $$x = 2$$, $$y = 17$$

Question 13

Solve the equation $$x^{2/3} = 16$ and check for extraneous solutions.

Accepted Answer

$$x = 64$$

Question 14

Given $$f(x) = 7x^2$ and g(x$$) = \frac{x - 8}{5}$$, evaluate (f$$ \circ g)(3)$$.

Accepted Answer

$$7 \left(\frac{3 - 8}{5}\$$right)^2$$ = 7 \left(\frac{-5}{5}\$$right)^2$$ = 7 	imes 1 = 7$$

Question 15

Find the inverse of $$f(x) = 49x^2$ for x$$ \geq 0$$.

Accepted Answer

$$f^{-1}(x$$) = \sqrt{\frac{x}{49}}$$

Question 16

A chemical reaction is modeled by $$y = (x + 2)^2$ - 4$$, where $$y is $$the concentration and $$x is $$time in hours. What are the coordinates of the vertex?

Accepted Answer

$$(-2, -4)$$

Question 17

Suppose the graph of $$f(x) = \sqrt{x} is $$shifted down 2 units and to the left 3 units. What is the equation of the new graph?

Accepted Answer

$$y = \sqrt{x + 3} - 2$$

Question 18

Evaluate $$(f 	imes g)(-1)$$ for $$f(x) = x^2$ - 5x$$ and $$g(x) = 8 - x^3$.

Accepted Answer

$$(-1)^2 - 5(-1) = 1 + 5 = 6$, 8$$ - $$(-1)^3 = 8 + 1 = 9$, 6$$ 	imes 9 = 54$$

College Algebra Problem Bank 2 – Step-by-Step Study Guidance

Guida di studio - Domande di pratica

Study guide - Flashcard