The figure shows the graph of a function g for 0 ≤ x ≤ 5. Which of the following statements is true about the function g? The rate of change of g is positive and increasing. The rate of change of g is positive and decreasing. The rate of change of g is negative and increasing. The rate of change of g is negative and decreasing.

The rate of change of g is negative and increasing.

The figure shows the graph of a function k for 0 ≤ x ≤ 5. Which of the following statements is true about the function k?

The function k is increasing and the graph of k is concave down.

The table shows values for a function f at selected values of x. Which of the following claim and explanation statements best fit these data? The graph of f could be concave up because the average rates of change over consecutive equal-length input-value intervals are positive. The graph of f could be concave up because the average rates of change over consecutive equal-length input-value intervals are increasing. The graph of f could be concave down because the average rates of change over consecutive equal-length input-value intervals are negative. The graph of f could be concave down because the average rates of change over consecutive equal-length input-value intervals are decreasing.

The graph of f could be concave up because the average rates of change over consecutive equal-length input-value intervals are increasing.

The table shows values for a function k at selected values of x. Which claim and explanation best fit these data?

k is best modeled by a quadratic function, because the change in the average rates of change over consecutive equal-length input-value intervals is constant.

The table gives values of the polynomial function g at selected values of x. Which of the following statements about g could be true?

g is an odd function and g(-1) = 6.

The polynomial function p is given by p(x) = $$(x^2 + 4)(x^2 - 9)$$ . Which of the following describes the zeros of p?

p has exactly two distinct real zeros and two non-real zeros.

The function h is given by $$h(x) = x^4 - x^3 - 2x + 1$$ . Describe the end behavior of h.

lim x→−∞ h(x) = ∞ and lim x→∞ h(x) = ∞

End behavior of rational function: r(x) = $$\frac{{4x^2 + x − 2}}{{8x^2 − 3x + 1}}$$ . What happens as input values decrease without bound?

As the input values of r decrease without bound, the output values of r get arbitrarily close to 1/2.

Rational function r has zeros at x = -3 and x = 4. Which expression could be r?

$$\frac{{(x+3)(x-4)^2}}{{(x-3)(x+4)}}$$

The rational function r is given by r(x) = $$\frac{x+1}{(x-4)^{ }}$$ . Which of the following limit statements about r is correct? Options: $$\lim_{x→4^-}r(x)=∞$$ , $$\lim_{x→4^-}r(x)=−∞$$ , $$\lim_{x→−1^−}=∞$$ , $$\lim_{x→−1^−}r(x)=−∞$$

$$\lim_{x→4^-}r(x)=−∞$$ .

In the xy-plane, the graph of a rational function k has a hole at x = −3. It is known that lim(x→−3) k(x) = 4. Which of the following could define k(x)? Options: $$k(x) = \frac{(x−3)(x−1)}{(x−3)(x+2)}$$ , $$k(x) = \frac{4(x+3)(x−4)}{(x+3)(x−1)}$$ , $$k(x) = \frac{(x−4)(x+2)}{(x−4)(x−6)}$$ , $$k(x) = \frac{(x+3)(x−5)}{(x+3)(x+1)}$$

$$k(x) = \frac{(x+3)(x−5)}{(x+3)(x+1)}$$

Function with a graph in the xy-plane with a vertical asymptote at x = 1 and a hole at x = −2: f(x) = $$\frac{x^2−4x+3}{x^2+x+2}$$ g(x) = $$\frac{x^2+x−2}{x^2+3x+2}\ $$ h(x) = $$\frac{x^2 + 4x + 4}{x^2 + x - 2}$$ k(x) = $$\frac{x^2+4x+3}{x^2-x-2}$$

h(x) = $$\frac{x^2 + 4x + 4}{x^2 + x - 2}$$

Expand the expression $$(x - 4y)^5$$ using the binomial theorem.

$$x^5 - 5x^4(4y) + 10x^3(4y)^2 - 10x^2(4y)^3 + 5x(4y)^4 - (4y)^5$$

Answer A is the right answer Options: (A) x | f(x) −1 | −1 0 | −4 1 | −5 2 | −2, (B) x | f(x) −1 | 7 0 | 4 1 | 3 2 | 6, (C) x | f(x) 3 | −1 4 | −4 5 | −5 6 | −2, (D) x | f(x) 3 | 7 4 | 4 5 | 3 6 | 6

(A) x | f(x) −1 | −1 0 | −4 1 | −5 2 | −2

The functions f and g are defined for all real numbers such that g(x) = f(2x) + 1. Which sequence of transformations maps the graph of f to the graph of g in the xy-plane?

A horizontal dilation of the graph of f by a factor of 1/2 followed by a vertical translation of the graph of f by 1 unit.

Find a polynomial function that has a zero at 2, and a multiplicity of 2 for the zeros at 0 and -3.

$$f(x) = x^5 + 4x^4 - 3x^3 - 18x^2$$

Equation for the given graph?

$$y = \frac{1}{6}(x-2)^{2}(x+2)(x-3)$$

The table gives values of the sequence s n at selected values of n. Which of the following statements about s n is true?

s n could be an arithmetic sequence, because successive terms have a constant difference.

The function f is given by f(x) = $$4 * (\frac{2}{3})^x$$ . Which of the following describes the end behavior of f?

lim_{x→−∞} f(x) = ∞ and lim_{x→∞} f(x) = 0

The exponential function f is defined by f(x) = $$ab^x$$ , where a and b are positive constants. Which of the following statements is true?

f demonstrates exponential decay because a > 0 and 0

True statement about the exponential function g given by $$\frac{1}{2} \cdot 3^x$$ ?

g is always increasing, and the graph of g is always concave up.

AP PreCal Exam Review 1-102

Flashcard

•

Mathematics

•

11th Grade

•

Practice Problem

•

Hard

Meredith Sparrow

FREE Resource

Student preview

50 questions

Show all answers

FLASHCARD QUESTION

Front

The figure shows the graph of a function f for 0 ≤ x ≤ 9. How many points of inflection does the graph of f have?

Back

FLASHCARD QUESTION

Front

Which of the following statements about the graph of f is correct? Options: On the interval 7 < x < 9, f is positive and increasing., On the interval 7 < x < 9, f is positive and decreasing., On the interval 7 < x < 9, f is negative and increasing., On the interval 7 < x < 9, f is negative and decreasing.

Back

On the interval 7 < x < 9, f is negative and increasing.

FLASHCARD QUESTION

Front

Which of the following statements about the graph of f is correct? On the interval 1 < x < 3, f is increasing at an increasing rate., On the interval 1 < x < 3, f is increasing at a decreasing rate., On the interval 1 < x < 3, f is decreasing at an increasing rate., On the interval 1 < x < 3, f is decreasing at a decreasing rate.

Back

On the interval 1 < x < 3, f is decreasing at an increasing rate.

FLASHCARD QUESTION

Front

Which of the following statements about the graph of f is correct?

On the interval 0 < x < 1, f is increasing and the graph of f is concave up.
On the interval 0 < x < 1, f is increasing and the graph of f is concave down.
On the interval 0 < x < 1, f is decreasing and the graph of f is concave up.
On the interval 0 < x < 1, f is decreasing and the graph of f is concave down.

Back

On the interval 0 < x < 1, f is decreasing and the graph of f is concave down.

FLASHCARD QUESTION

Front

Which statement about the graph of f is correct on the interval 5 < x < 7?

Back

On the interval 5 < x < 7, the rate of change of f is negative and increasing.

FLASHCARD QUESTION

Front

The figure shows the graph of a function f for 0 ≤ x ≤ 5. Which of the following statements is true about the function f?

f is increasing at an increasing rate.
f is increasing at a decreasing rate.
f is decreasing at an increasing rate.
f is decreasing at a decreasing rate.

Back

f is increasing at an increasing rate.

FLASHCARD QUESTION

Front

The figure shows the graph of a function j for 0 ≤ x ≤ 5. Which of the following statements is true about the function j?

Back

The graph of j is increasing at a decreasing rate.

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