Understanding Intercepts in Functions

The video tutorial covers how to find y-intercepts and x-intercepts of various equations. It begins with an introduction to y-intercepts, explaining that they occur where the graph crosses the y-axis, and provides examples using cubic, absolute value, and linear equations. The tutorial then shifts to x-intercepts, explaining that they occur where the graph crosses the x-axis, and provides examples using quadratic and cubic functions. The video emphasizes the importance of setting the opposite variable to zero to find intercepts.

What is the y-intercept of the function f(x) = (x - 2)^3 + 1?

• (0, 2)

• (0, -1)

• (0, 1)

• (0, -7)

How do you find the y-intercept of an absolute value function?

• Use the slope-intercept form

• Set y = 0 and solve for x

• Set x = 0 and solve for y

• Find the vertex of the function

What is the y-intercept of the linear equation y = x - 4 + 1?

• (0, 1)

• (0, 4)

• (0, -4)

• (0, -3)

What is the y-intercept of the cubic function f(x) = (x + 4)^3 - 2?

• (0, 64)

• (0, 4)

• (0, -2)

• (0, 62)

What does an x-intercept represent on a graph?

• The lowest point on the graph

• Where the graph crosses the y-axis

• The highest point on the graph

• Where the graph crosses the x-axis

How do you find the x-intercept of a function?

• Use the quadratic formula

• Find the slope of the function

• Set x = 0 and solve for y

• Set y = 0 and solve for x

What is the x-intercept of the quadratic function f(x) = (x - 5)^2?

• (0, -5)

• (-5, 0)

• (5, 0)

• (0, 5)

How many x-intercepts can a quadratic function have?

• None

• Exactly one

• One or two

• Exactly two

What is the x-intercept of the cubic function f(x) = (x + 6)^3?

• (-6, 0)

• (6, 0)

• (0, 6)

• (0, -6)

What is the significance of the vertex in finding x-intercepts of a quadratic function?

• It may touch the x-axis at the vertex

• It determines the slope

• It is irrelevant

• It is the midpoint of the intercepts