Front

What is a vertical shift in a function?

Back

A vertical shift occurs when a constant is added to or subtracted from a function, moving it up or down on the graph. For example, if f(x) = x^2, then f(x) + 4 shifts the graph 4 units up.

Front

What is a horizontal shift in a function?

Back

A horizontal shift occurs when a constant is added to or subtracted from the input of a function, moving it left or right on the graph. For example, f(x) = (x - 2)^2 shifts the graph 2 units to the right.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y = 0. If they are equal, divide the leading coefficients.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean for a function to have no x-intercept?

Back

A function has no x-intercept if it does not cross the x-axis, meaning there are no real solutions to the equation f(x) = 0.

Tags

CCSS.HSF-IF.C.7E

Front

What is rotational symmetry in a function?

Back

Rotational symmetry in a function means that the graph looks the same when rotated 180 degrees around a point. For example, the function f(x) = -x^2 has rotational symmetry about the origin.

Tags

CCSS.HSF.BF.B.3

Front

What is the exponential form of a logarithmic equation?

Back

The exponential form of a logarithmic equation log_b(a) = c is b^c = a. For example, log_6(36) = 2 translates to 6^2 = 36.

Tags

CCSS.HSF.BF.B.5

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is found by evaluating the function at x = 0.

Front

What is the difference between increasing and decreasing functions?

Back

An increasing function has a positive slope and rises as x increases, while a decreasing function has a negative slope and falls as x increases.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.