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AP Calculus AB MCQ Bank — Preview 0 / 5 answered
1
Intermediate Passage 1: AP Calculus AB Exam 1 - Page 1

aGraph of f

The graph of a function $f$ is shown above. Which of the following statements about $f$ is false?

A
$f$ is continuous at $x = a$.
B
$f$ has a relative maximum at $x = a$.
C
$x = a$ is in the domain of $f$.
D
$\lim_{x \to a^+} f(x)$ is equal to $\lim_{x \to a^-} f(x)$
E
$\lim_{x \to a} f'(x)$ exists
2
Intermediate Passage 2: AP Calculus AB Exam 1 - Page 2

$$f(x) = \begin{cases} 2 - 3x & \text{for } x \le 2 \\ kx + 1 & \text{for } x > 2 \end{cases}$$

The function $f$ is defined above. For what value of $k$, if any, is $f$ continuous at $x = 2$ ?

A
$-\frac{5}{2}$
B
$-\frac{3}{2}$
C
$0$
D
$1$
E
No value of $k$ will make $f$ continuous at $x = 2$.
3
Intermediate Passage 3: AP Calculus AB Exam 1 - Page 3

Let $f$ be the function given by $f(x) = \frac{(x-2)(x+3)}{(x-2)(x+1)}$. For which of the following values of $x$ is $f$ not continuous?

A
$-3$ and $-1$ only
B
$-3$, $-1$, and $2$
C
$-1$ only
D
$-1$ and $2$ only
E
$2$ only
4
Intermediate Passage 4: AP Calculus AB Exam 1 - Page 4

What are the equations of the horizontal asymptotes of the graph of $y = \frac{3x}{\sqrt{x^2-1}}$ ?

A
$y = 0$ only
B
$y = 3$ only
C
$y = -3$ only
D
$y = 3$ and $y = -3$
E
$y = 1$ and $y = -1$
5
Intermediate Passage 5: AP Calculus AB Exam 1 - Page 5
$x$$0$$1$$2$
$f(x)$$1$$k$$2$

The function $f$ is continuous on the closed interval $[0, 2]$ and has values that are given in the table above. The equation $f(x) = \frac{1}{2}$ must have at least two solutions in the interval $[0, 2]$ if $k =$

A
$0$
B
$\frac{1}{2}$
C
$1$
D
$2$
E
$3$
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