Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Tags

CCSS.HSF-IF.C.7D

Front

Identify the vertical asymptote of the function f(x) = \frac{1}{x+2}.

Back

The vertical asymptote is x = -2.

Tags

CCSS.HSF-IF.C.7D

Front

What is the sign analysis chart used for?

Back

A sign analysis chart is used to determine the intervals where a polynomial function is positive or negative by analyzing the signs of the function's factors.

Front

Given the polynomial p(x) = -x(x-4)(x+2), find the intervals where p(x) ≥ 0.

Back

The intervals are (-∞, -2] ∪ [0, 4].

Front

What does the average rate of change represent?

Back

The average rate of change of a function over an interval [a, b] is given by the formula \frac{f(b) - f(a)}{b - a}, representing the slope of the secant line between the points (a, f(a)) and (b, f(b)).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

Where is the average rate of change negative for the function f(x)?

Back

The average rate of change is negative in the interval (0.3, 3).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What are the vertical asymptotes of the function f(x) = \frac{1}{x^2 - 25}?

Back

The vertical asymptotes are x = 5 and x = -5.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine where the average rate of change is decreasing?

Back

To determine where the average rate of change is decreasing, analyze the intervals where the derivative of the function is negative.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the significance of the roots of a polynomial function?

Back

The roots of a polynomial function are the values of x where the function equals zero, indicating the x-intercepts of the graph.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants and n is a non-negative integer.