Understanding Y-Intercepts in Exponential Functions

The video tutorial explains how to find the Y-intercept of exponential functions. It begins by defining the Y-intercept as the point where the graph crosses the y-axis, which occurs when x equals zero. The tutorial then demonstrates finding the Y-intercept for two exponential functions. For the first function, setting x to zero results in a Y-intercept of (0, 4). For the second function, the Y-intercept is (0, 27). The video concludes by verifying these results using graphs, with the red graph representing the first function and the blue graph representing the second.

What is the y-intercept of a graph?

• The highest point on the graph

• The point where the graph crosses the y-axis

• The lowest point on the graph

• The point where the graph crosses the x-axis

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

• Set y to zero and solve for x

• Set x to zero and solve for y

• Find the maximum value of the function

• Find the minimum value of the function

What is the y-intercept of the first exponential function given by y = 3^0 + 3?

• (0, 1)

• (0, 4)

• (0, 3)

• (0, 6)

In the first exponential function, why is the plus three not part of the exponent?

• Because it is part of the exponent

• Because it is a constant multiplier

• Because it is added after calculating the power

• Because it is part of the base

What is the y-intercept of the second exponential function given by y = 3^(0+3)?

• (0, 81)

• (0, 27)

• (0, 9)

• (0, 3)

How can you verify the y-intercept of an exponential function?

• By finding the x-intercept

• By calculating the derivative

• By looking at the graph where it crosses the y-axis

• By checking the slope of the graph