Q: Which of the following best describes the end behavior of $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

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

Question 1

Given the function $$f(x) = 2x^2$ - 8x + 6$$, what are the $$x-$$intercepts of the graph?

Accepted Answer

Question 2

Which of the following functions is symmetric with respect to the $$y-$$axis?

Accepted Answer

$$f(x) = x^2$

Question 3

If $$f(x) = x^2$ - 4x + 7$$, what is the minimum value of $$f(x)$$ and at what $$x$$ does it occur?

Accepted Answer

Minimum at $$x = 2$$, $$f(2) = 3$$

Question 4

Given $$f(x) = x^3$ - 2x^2$ + x - 2$$, use the Rational Zero Theorem to determine which of the following is a possible rational zero.

Accepted Answer

$$x = 2$$

Question 5

A function $$f is $$defined by $$f(x) = \sqrt{9 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$[-3, 3]$$

Question 6

Which of the following statements is true about the function $$f(x) = x^4$ - 2x^2$ + 1$$?

Accepted Answer

It is an even function.

Question 7

Given $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 1$

Question 8

A polynomial $$p(x) of $$degree 4 has zeros at $$x = 1 ($$multiplicity 2), $$x = -2$$, and $$x = 3. $$Which of the following could be $$p(x)$$?

Accepted Answer

$$(x - 1)^2$(x + 2)(x - 3)$$

Question 9

Which of the following best describes the end behavior of $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

Accepted Answer

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

Question 10

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$\frac{f}{g}(x)$$?

Accepted Answer

$$x - 2$$

Question 11

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$What is the maximum height reached by the ball?

Accepted Answer

$$16 ft$$

Question 12

Given $$f(x) = x^2$ + 2x + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(-1, 4)$$

Question 13

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

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

Question 14

If $$f(x) = x^2$ - 1$$ and $$g(x) = x - 1$$, what is the domain of $$\frac{f}{g}(x)$$?

Accepted Answer

$$x 
eq 1$$

Question 15

Given the polynomial $$f(x) = x^4$ - 5x^2$ + 4$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 4$$

Question 16

Which of the following describes the graph of $$f(x) = |x - 3|$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 0)$$

Question 17

If $$f(x) = x^2$ + 1$$ and $$g(x) = 2x$$, what is $$(f + g)(x)$$?

Accepted Answer

$$x^2 + 2x + 1$

Question 18

Which of the following is the correct application of the Factor Theorem?

Accepted Answer

If $$f(a) = 0$$, then $$(x - a) is a $$factor of $$f(x)$$

Question 19

Given $$f(x) = x^2$ - 2x + 1$$, which of the following statements is true?

Accepted Answer

The graph touches the $$x-$$axis at $$x = 1$$ and does not cross it.

Precalculus Study Guide: Algebraic and Polynomial Functions (Exam 1 Objectives)

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