Question 1

Which transformation is applied to the graph of $$f(x) = x^2$ to obtain g(x) = (x$$ - $$2)^2 + 3$?

Accepted Answer

Shift right 2 units and up 3 units

Question 2

What is the domain of the function $$g(x) = \dfrac{2x}{x^2$ - 64}$$?

Accepted Answer

$$(-\infty, -8) \cup (-8, 8) \cup (8, \infty)$$

Question 3

A company’s cost to manufacture $$x$$ thousand automobiles is $$C(x) = 4x^2$ - 32x + 128. $$How many automobiles must be produced to minimize the cost?

Accepted Answer

$$4$$ thousand

Question 4

Given $$f(x) = (x - 3)^2$ - 3$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, -3)$$

Question 5

You have $$92$$ feet of fencing to enclose a rectangular plot that borders a river (no fence along the river). What are the dimensions that maximize the area?

Accepted Answer

Length $$= 46 ft$$, Width $$= 23 ft$$

Question 6

What is the range of $$f(x) = (x + 4)^2$ + 7$$?

Accepted Answer

$$[7, \infty)$$

Question 7

For the polynomial $$f(x) = 4x^3$ - 2x^2$ - 2x - 1$$, what is the end behavior as $$x 	o \pm \infty$$?

Accepted Answer

Falls to the left and rises to the right

Question 8

Solve the inequality $$(x - 2)(x + 9) \u003e 0$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -9) \cup (2, \infty)$$

Question 9

A person throws a baseball from the top of a $$208-$$foot building. The height is modeled by $$s(t) = -16t^2$ + 64t + 208. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$2$$ seconds

Question 10

What is the degree of the polynomial $$f(x) = -2x + 6x^4$?

Accepted Answer

$$4$$

Question 11

For the polynomial $$f(x) = x^4$ - 9x^2$, how many turning points can its graph have at most?

Accepted Answer

Question 12

For the rational function $$f(x) = \dfrac{1}{x^2$ - 4}$$, what are the vertical asymptotes?

Accepted Answer

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

Question 13

Which of the following describes the symmetry of $$f(x) = x^4$ - 9x^2$?

Accepted Answer

Y-axis symmetry

Question 14

For the polynomial $$f(x) = (x + 1)(x - 8)(x - 1)^2$, which zero does the graph touch the x-axis and turn around?

Accepted Answer

$$x = 1$$

Question 15

What is the solution set for the rational inequality $$\dfrac{x - 5}{x + 3} \u003c 0$$?

Accepted Answer

$$(-3, 5)$$

Question 16

For the polynomial $$f(x) = 3x^4$ - 2x^2$, what is the end behavior as x$$ 	o \pm \infty$$?

Accepted Answer

Rises to the left and rises to the right

Question 17

The owner of a video store has profits $$P(x) = -x^2$ + 130x + 70$$, where $$x is $$the number of videos rented daily. What is the maximum profit to the nearest dollar?

Accepted Answer

$$4,295$$

Question 18

For the quadratic function $$f(x) = 2x^2$ - 2x - 8$$, does it have a minimum or maximum value, and what are the coordinates of that point?

Accepted Answer

Minimum at $$\left(\dfrac{1}{2}, -\dfrac{17}{2}\right)$$

Question 19

What is the solution set for the polynomial inequality $$x^2 - 3x - 10$$ \leq 0$$?

Accepted Answer

$$[-2, 5]$$

College Algebra Practice: Transformations, Quadratics, Polynomials, and Inequalities

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