Finding Intercepts and Function Shifts

The video tutorial explains how to graph the function f(x-2) by using function notation and substitution. It covers the process of finding x-intercepts and y-intercepts, and demonstrates how to use factorization to simplify the process. The tutorial also explains the concept of graph translation, showing how the graph of f(x) shifts horizontally when transformed to f(x-2).

What does the function notation f(x-2) imply?

• Replace x with x+2

• Replace x with x-2

• Multiply x by 2

• Divide x by 2

When replacing x with x-2 in f(x), what is the new expression for x squared?

• (x+2) squared

• (x-2) squared

• x squared

• 2x squared

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

• Set y to zero and solve for x

• Find the minimum value of the function

• Find the maximum value of the function

• Set x to zero and solve for y

What is the significance of factorizing a function when finding intercepts?

• It makes the function more complex

• It simplifies the process of finding intercepts

• It changes the function's shape

• It eliminates the intercepts

How do you determine the y-intercept of a function?

• Set x to zero and solve for y

• Set y to zero and solve for x

• Find the derivative of the function

• Integrate the function

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

• -6

• 12

• 0

• -12

What does a translation of a graph involve?

• Scaling the graph

• Reflecting the graph

• Rotating the graph

• Shifting the graph horizontally or vertically

How many units is the graph of f(x-2) shifted compared to f(x)?

• 1 unit to the left

• 2 units to the right

• 2 units to the left

• 3 units to the left

What is the effect of a horizontal shift on the x-intercepts of a function?

• They shift horizontally

• They move vertically

• They disappear

• They remain unchanged

What is the new x-intercept of the function after a horizontal shift of 2 units to the right?

• 0 and 1

• 1 and 2

• 2 and 3

• -1 and 0