Question 1

Given the piecewise function $$f(x) = \begin{cases} 5x - 2 & 	ext{if } x \u003c 2 \ x^2$ - 1 & 	ext{if } x \geq 2 \end{cases}$$, which of the following statements is TRUE about the graph of $$f(x)$$?

Accepted Answer

The graph has a jump discontinuity at $$x = 2.$$

Question 2

Let $$f(x) = x. $$Which of the following is the correct expression for $$g(x)$$, where $$g(x) is $$the graph of $$f(x)$$ shifted left 3 units and down 2 units?

Accepted Answer

$$g(x) = (x + 3) - 2$$

Question 3

Consider the quadratic function $$f(x) = 4x^2$ + 9x + 2. $$What is the vertex of the parabola?

Accepted Answer

$$\left(-\frac{9}{8}, -\frac{49}{16}\right)$$

Question 4

Given the circle $$x^2$$ + $$y^2 + 4x - 12y + 15 = 0$, what is the center and radius of the circle?

Accepted Answer

Center: $$(-2, 6)$$, Radius: $$5$$

Question 5

For the rational function $$f(x) = \frac{x^2$ + 6}{x - 4}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 4$$

Question 6

Solve the inequality $$4x - 3 \leq 2. $$What is the solution in interval notation?

Accepted Answer

$$(-\infty, 1.25]$$

Question 7

Solve the equation $$x^2 + 2x - 15 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = 3$$ and $$x = -5$$

Question 8

Let $$f(x) = 5 - x$$ and $$g(x) = \frac{1}{x + 2}. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$5 - \frac{1}{x + 2}$$

Question 9

Given the cubic function $$f(x) = 2x^3$ - 5x^2$ + 4x - 3$$, which of the following lists all possible rational zeros according to the Rational Root Theorem?

Accepted Answer

$$\pm1, \pm3, \pm\frac{1}{2}, \pm\frac{3}{2}$$

Question 10

A polynomial $$f(x)$$ has zeros at $$5$$, $$2i$$, and $$2$$ with multiplicity $$3. $$Which of the following is the correct factored form for $$f(x)$$ with real coefficients and minimal degree?

Accepted Answer

$$(x - 5)(x^2$ + 4)(x - 2)^3$

Question 11

The cost function for manufacturing $$x$$ cellphones is $$C(x) = 8x^2$ - 320x + 6000. $$How many cellphones should be manufactured to minimize the cost?

Accepted Answer

$$40$$

Question 12

The volume $$V of a $$gas varies inversely as pressure $$P$$ and directly as temperature $$T in $$degrees K. If $$V = 1.6 L at$$ $$T = 300 K $$and $$P = 15 Pa$$, what is the volume at $$T = 340 K $$and $$P = 20 Pa$$?

Accepted Answer

$$1.36 L$$

Question 13

For the function $$f(x) = 4x^2$ + 9x + 2$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = -\frac{9}{8}$$

Question 14

For the rational function $$f(x) = \frac{x^2$ + 6}{x - 4}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 15

Solve the inequality $$x^2 + 2x - 12$$ \leq 3$$. What is the solution set in interval notation?

Accepted Answer

$$[-5, 2]$$

Question 16

For the function $$f(x) = 4x^2$ + 9x + 2$$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$\left[-\frac{49}{16}, \infty\right)$$

Question 17

For the function $$f(x) = 4x^2$ + 9x + 2$$, on which interval is the function increasing?

Accepted Answer

$$\left(-\frac{9}{8}, \infty\right)$$

Question 18

Let $$f(x) = 5 - x$$ and $$g(x) = \frac{1}{x + 2}. $$What is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x 
eq -2$$

Question 19

A manufacturer wants to minimize the cost function $$C(x) = 8x^2$ - 320x + 6000. $$What is the minimum cost?

Accepted Answer

$$3200$$

College Algebra Midterm Review Guidance

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