Question 1

Which of the following is the domain of the function $$f(x) = \dfrac{3x-1}{7x+4}$$?

Accepted Answer

$$(-\infty, -\dfrac{4}{7}) \cup (-\dfrac{4}{7}, \infty)$$

Question 2

Find the domain of the function $$h(x) = \sqrt{-7x+11}.$$

Accepted Answer

$$(-\infty, \dfrac{11}{7}]$$

Question 3

Let $$f(x) = 4 + \dfrac{2}{x}$$ and $$g(x) = \sqrt{5x}. $$What is the domain of $$(f+g)(x)$$?

Accepted Answer

$$\{x \mid x \u003e 0\}$$

Question 4

Given the piecewise function $$f(x) = \begin{cases} x+3 & x \u003c -1 \ |x| & -1 \leq x \u003c 1 \ -x+2 & x \geq 1 \end{cases}$$, what is $$f(1)$$?

Accepted Answer

$$1$$

Question 5

Which of the following graphs does NOT represent a function?

Accepted Answer

A graph where some vertical line crosses the graph at more than one point

Question 6

Suppose $$h(x) = \sqrt{3x+1}. $$For which value of $$x$$ does $$h(x) = 5$$?

Accepted Answer

$$x = 8$$

Question 7

Given $$Q(x) = -x^2$ - 2x + 8$$, what is the vertex of the parabola?

Accepted Answer

$$(-1, 9)$$

Question 8

A landscaper has 100 ft of stone to build a wall on three sides of a rectangular garden (the fourth side is the house). If $$x is $$the length of the side perpendicular to the house, which function models the area $$A(x) of $$the garden?

Accepted Answer

$$A(x) = x(100-2x)$$

Question 9

Given the function $$g(x) = 3x^2$ + 12x - 2$$, does it have a maximum or minimum value, and what is the value?

Accepted Answer

Minimum at $$x = -2$$, value $$-14$$

Question 10

Which of the following describes the transformation of $$y = x^3$ to y$$ = \dfrac{1}{3}(- $$(x+2)^3) + 1$?

Accepted Answer

Shift left 2, reflect over $$y-$$axis, shrink vertically by 3, shift up 1

Question 11

Given $$f(x) = 4 + \dfrac{2}{x}$$ and $$g(x) = \sqrt{5x}$$, what is $$(g-f)(5)$$?

Accepted Answer

$$\sqrt{25} - (4 + \dfrac{2}{5}) = 5 - 4.4 = 0.6$$

Question 12

Which of the following is the range of the piecewise function $$f(x) = \begin{cases} x+3 & x \u003c -1 \ |x| & -1 \leq x \u003c 1 \ -x+2 & x \geq 1 \end{cases}$$?

Accepted Answer

$$[0, \infty)$$

Question 13

For the quadratic function $$Q(x) = -x^2$ - 2x + 8$$, what is the range?

Accepted Answer

$$(-\infty, 9]$$

Question 14

Given the function $$s(x) = \dfrac{x^2$ - 1}{\sqrt{-3 + 5x}}$$, what is the domain?

Accepted Answer

$$\left(\dfrac{3}{5}, \infty\right)$$

Question 15

Suppose a function $$C(t)$$ models the concentration of insulin in a patient's blood over time. If $$C(0) = 10$$, what does this value represent?

Accepted Answer

The initial concentration of insulin in the patient's blood

Question 16

Which of the following data sets can be modeled by a linear function?

Accepted Answer

Data set where the average rate of change between all pairs of points is the same

Question 17

Given $$h(x) = -3\left(\dfrac{1}{2}x-1\$$right)^2$$ + 4$$, which transformation is NOT applied to the parent function $$y = x^2$?

Accepted Answer

Horizontal shift right by 2

Question 18

If $$A(x) = x(100-2x)$$ models the area of a garden with 100 ft of wall on three sides, for which $$x is $$the area maximized?

Accepted Answer

$$x = 25$$

Question 19

Given the quadratic function $$y = ax^2$ + bx + c$$, which of the following gives the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = -\dfrac{b}{2a}$$

College Algebra Exam 2 Review: Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards