Question 1

Given the graph in Question 1a, what is the minimum degree of the polynomial and the sign of the leading coefficient?

Accepted Answer

Degree 3, negative leading coefficient

Question 2

For $$f(x) = (x-2)(x+1)^3$, what is the multiplicity of each zero?

Accepted Answer

Zero at $$x=2$$ with multiplicity 1, zero at $$x=-1$$ with multiplicity 3

Question 3

Solve for $$x$$: $$1 = 2x - \frac{1}{x}$$

Accepted Answer

$$x = 1 or$$ $$x = -\frac{1}{2}$$

Question 4

Given $$f(x) = \frac{5x^2$}{x^2$-4}$$, what are the vertical and horizontal asymptotes?

Accepted Answer

Vertical: $$x=2$$, $$x=-2$$; Horizontal: $$y=5$$

Question 5

Ohm's law states $$I = \frac{k}{R}. If$$ $$I=9$$ when $$R=2$$, what is $$I$$ when $$R=3$$?

Accepted Answer

$$I = 6$$

Question 6

For $$g(x) = \frac{5x^2$}{x-2}$$, what is the horizontal asymptote?

Accepted Answer

No horizontal asymptote

Question 7

Given $$f(x) = \frac{5x-1}{x^2$+4}$$, what is the horizontal asymptote?

Accepted Answer

$$y=0$$

Question 8

If the maximum weight $$W a $$wooden beam can support varies directly as the square of its height $$H$$, and a beam of height 1 ft supports 4 tons, what is the weight supported by a beam of height 1.5 ft?

Accepted Answer

$$W = 9$$ tons

Question 9

Given $$f(x) = \frac{1}{x-5}$$, what transformation has been applied to the base function $$y = \frac{1}{x}$$?

Accepted Answer

Shift right by 5 units

Question 10

For the function $$N(t) = \frac{40 + 20t}{1 + 0.03t^2$}$$, what is the horizontal asymptote?

Accepted Answer

$$y=0$$

Question 11

Given $$C(x) = 9x + 14$$ and $$P(x) = -0.3x^2$ + 47x - 14$$, what is $$R(x)$$, the total revenue function?

Accepted Answer

$$R(x) = -0.3x^2$ + 56x$$

Question 12

If $$f(x) = \sqrt{x} + 1$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = $$(x-1)^2$$

Question 13

Given $$f(x) = \frac{1}{x}$$ and $$g(x) = x+7$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = \frac{1}{x+7}$$

Question 14

If $$f(x) = \frac{1}{x-3}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{1}{x} + 3$$

Question 15

Given the function $$f(x)$$ defined by the table: $$x: -10, -6, -1, 3, 7$$ and $$f(x): -6, -2, 1, 7, 15$$, what is $$f^{-1}(7$$)$$?

Accepted Answer

$$f^{-1}(7) = 3$

Question 16

If the light intensity $$I at a $$distance $$d$$ from a source varies inversely as the square of the distance, and $$I=8 at$$ $$d=3$$, what is $$I at$$ $$d=2$$?

Accepted Answer

$$I = 12$$

Question 17

Given Hooke's law $$D = kW$$, if a weight of 40 pounds stretches the spring 5 inches, what is the distance stretched by a 65-pound weight?

Accepted Answer

$$D = 8.125$$ inches

Question 18

If $$f(x) = \frac{1}{x}$$ and $$g(x) = x+7$$, what is $$(g \circ f)(x)$$?

Accepted Answer

$$(g \circ f)(x) = \frac{1}{x} + 7$$

Question 19

A contractor charges $$50$$ per hour plus $$5950 in $$material costs. What does $$f^{-1}(x$$)$$ calculate for f(x) = 50x + 5950$?

Accepted Answer

The number of hours worked given the total cost

Comprehensive Study Guide: College Algebra Core Concepts and Applications

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