Understanding Graph Shifts

The video tutorial explains how to match graphs with their corresponding functions based on transformations of the basic function f(x) = e^x. It covers horizontal and vertical shifts, determined by the values of C and D, respectively. Positive C values shift the graph left, while negative C values shift it right. Positive D values shift the graph up, and negative D values shift it down. The tutorial provides examples of graph matching, illustrating how these transformations affect the graph's position relative to the original function.

What is the basic function used as a reference for graph shifts in this tutorial?

• f(x) = ln(x)

• f(x) = x^2

• f(x) = e^x

• f(x) = sin(x)

If the value of C is positive, in which direction does the graph shift?

• Left

• Down

• Up

• Right

What happens to the graph when C is negative?

• It shifts down

• It shifts left

• It shifts up

• It shifts right

When D is positive, how does the graph move?

• Down

• Up

• Right

• Left

What is the effect on the graph when D is negative?

• It shifts down

• It shifts up

• It shifts right

• It shifts left

For the function y = e^(x+2), what is the value of C and the direction of the shift?

• C = -2, shift left

• C = 2, shift right

• C = 2, shift left

• C = -2, shift right

In the function y = e^x + 2, what does the +2 indicate?

• Horizontal shift left

• Horizontal shift right

• Vertical shift up

• Vertical shift down

For the function y = e^(x-2), what is the value of C and the direction of the shift?

• C = -2, shift left

• C = 2, shift right

• C = 2, shift left

• C = -2, shift right

In the function y = e^x - 2, what does the -2 indicate?

• Horizontal shift right

• Horizontal shift left

• Vertical shift up

• Vertical shift down

Which graph corresponds to a shift down by two units?

• Graph C

• Graph B

• Graph A

• Graph D