Page 1 Memorization Quiz

Question 1

What happens to functions when they are concave up?

Answer 1

Functions change at an increasing rate

Concavity indicates the rate of change of the function’s slope.

Question 2

What happens to functions when they are concave down?

Answer 2

Functions change at a decreasing rate

Concavity affects the behavior of the function’s slope.

Question 3

Write the limit in proper notation for a function whose y-values increase towards ∞ as its x-values decrease toward -∞.

Answer 3

lim x→-∞ f(x) = ∞

This notation expresses the behavior of the function at infinity.

Question 4

What is the formula for average rate of change?

Answer 4

(f(b) - f(a)) / (b - a)

The average rate of change measures the change in the function’s value over an interval.

Question 5

Write a limit that proves a function has a horizontal asymptote at y = 3.

Answer 5

lim x→∞ f(x) = 3

This shows that the function approaches a constant value as x approaches infinity.

Question 6

Write a limit that proves a function has a vertical asymptote at x=3.

Answer 6

lim x→ ±3 f(x) = ±∞

This indicates that the function’s values grow without bound as x approaches 3.

Question 7

Where are vertical asymptotes found?

Answer 7

Vertical asymptotes are found where the denominator only is zero

This condition typically indicates a division by zero in rational functions.

Question 8

Where are holes found in a function?

Answer 8

Holes are found where the numerator and denominator are both zero

This occurs when a factor cancels out in a rational function.

Question 9

What are the rules for finding horizontal asymptotes?

Answer 9

a. If numerator degree > denominator degree, there isn’t one!
* b. If numerator degree < denominator degree, y = 0
* c. If numerator degree = denominator degree, y = ratio of leading coefficients

These rules help determine the end behavior of rational functions.

Question 10

How are slant asymptotes found?

Answer 10

Slant asymptotes are found using long division

This method is used when the degree of the numerator is one more than that of the denominator.

Question 11

What are the transformations of
y = -a • f(-b(x + C)) + d

Answer 11

Reflects over x-axis, vertical dilation, reflects over y-axis, horizontal dilation (opposite), horizontal translation (opposite), vertical translation

Each parameter affects the graph’s position and shape according to transformations.

Question 12

What is the definition of an even function?

Answer 12

f(-x) = f(x)

Even functions are symmetric about the y-axis.

Question 13

What is the definition of an odd function?

Answer 13

f(-x) = -f(x)

Odd functions are symmetric about the origin.