Q: For the polynomial $$f(x) = x(x-2)^2$(x+1)$$, which of the following describes its end behavior?

As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Q: A polynomial $$f(x)$$ has zeros at $$x = 2 ($$multiplicity 1) and $$x = 1 ($$multiplicity 2), $$y-$$intercept at $$(0, -4)$$, and degree 3. What is the end behavior of $$f(x)$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Q: Which of the following best describes the end behavior of $$f(x) = -x^4$ + 2x^3$ - x^2$ + 5$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Given the quadratic function $$f(x) = -x^2$ + 4x - 3$$, which of the following statements about its graph is correct?

Accepted Answer

The graph opens downward and has a maximum vertex.

Question 2

A polynomial has zeros at $$x = -3 ($$multiplicity 2), $$x = 1 ($$multiplicity 1), and $$x = 4 ($$multiplicity 1). Its $$y-$$intercept is $$(0, -12)$$ and its degree is 4. Which equation could represent this polynomial?

Accepted Answer

$$f(x) = a(x+3)^2$(x-1)(x-4)$$, where $$a is $$chosen so $$f(0) = -12$$

Question 3

The revenue function for a product is $$R(p) = -3p^2$ + 120p$$, where $$p is $$the price in dollars. What price $$p$$ maximizes the revenue?

Accepted Answer

$$p = 20$$

Question 4

For the polynomial $$f(x) = x(x-2)^2$(x+1)$$, which of the following describes its end behavior?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 5

A rectangular garden is to be built with one side against a house. If you have 60 feet of fencing for the other three sides, what is the maximum area you can enclose?

Accepted Answer

The maximum area is $$A = 300$$ square feet.

Question 6

Solve the inequality $$\dfrac{10x + 2}{x^2$ - 3x + 4} \u003e 0. $$Which of the following describes the solution set?

Accepted Answer

All real $$x$$ except $$x = -0.2$$

Question 7

Given $$g(x) = 3x^2$(x-1)^4(x+1$$)$, what is the degree of the polynomial?

Accepted Answer

Degree 7

Question 8

For the rational function $$h(x) = \dfrac{x^2$ - 9}{x^2$ - 3x + 2}$$, which of the following is a vertical asymptote?

Accepted Answer

$$x = 1$$ and $$x = 2$$

Question 9

A polynomial $$f(x)$$ has zeros at $$x = 2 ($$multiplicity 1) and $$x = 1 ($$multiplicity 2), $$y-$$intercept at $$(0, -4)$$, and degree 3. What is the end behavior of $$f(x)$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 10

For the quadratic function $$f(x) = -x^2$ + 4x - 3$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 2$$

Question 11

Which of the following best describes the effect of multiplicity on the graph of a polynomial at a zero?

Accepted Answer

If the zero has even multiplicity, the graph touches and turns at the $$x-$$axis.

Question 12

Given the polynomial $$f(x) = x^3$ - 4x^2$ + 2x$$, which of the following is a critical number?

Accepted Answer

$$x = 2$$

Question 13

For the rational function $$h(x) = \dfrac{x^2$ - 9}{x^2$ - 3x + 2}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 1$$

Question 14

A polynomial $$f(x)$$ has zeros at $$x = -2 ($$multiplicity 2), $$x = 1 ($$multiplicity 1), $$y-$$intercept at $$(0, -4)$$, and degree 3. Which of the following is the correct equation for $$f(x)$$?

Accepted Answer

$$f(x) = a(x+2)^2$(x-1)$$, where $$a is $$chosen so $$f(0) = -4$$

Question 15

For the quadratic function $$f(x) = -x^2$ + 4x - 3$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -3)$$

Question 16

Which of the following is true about the graph of $$f(x) = x(x-2)^2$(x+1) at$$ $$x = -2$$?

Accepted Answer

The graph touches and turns at $$x = -2.$$

Question 17

For the polynomial $$g(x) = 3x^2$(x-1)^4(x+1$$)$$, what is the multiplicity of the zero at x = -1$?

Accepted Answer

Multiplicity 1

Question 18

Which of the following best describes the end behavior of $$f(x) = -x^4$ + 2x^3$ - x^2$ + 5$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Precalculus Practice: Polynomial, Quadratic, and Graph Analysis Study Notes

Study Guide - Practice Questions

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