Precalculus Review

Front

What is a transformation in the context of graphing functions?

Back

A transformation refers to the changes made to the parent graph of a function, which can include translations (shifts), reflections, stretches, and compressions.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the corresponding point on the reflected graph will be (x, -y).

Front

If a function f(x) passes through the point (1, 4), what point does its inverse f^-1(x) pass through?

Back

The inverse function f^-1(x) will pass through (4, 1) because the x and y coordinates are switched.

Tags

CCSS.HSF-BF.B.4C

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

Back

The horizontal asymptote is y = 2, as the degrees of the numerator and denominator are the same.

Tags

CCSS.HSF-IF.C.7D

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if f(a) = b, then f^-1(b) = a.

Tags

CCSS.HSF-BF.B.4A

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, switch the x and y in the equation and solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of the original function becomes the range of its inverse, and vice versa.

Tags

CCSS.HSF-BF.B.4C

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x₁ and x₂ in that interval, if x₁ < x₂, then f(x₁) < f(x₂).

Front

What is the increasing interval for the function f(x) = x² - 4x + 3?

Back

The increasing interval is (-∞, 2) because the vertex of the parabola is at x = 2, and the function increases after this point.