Exponential Functions and Their Graphs

The video tutorial explains how to draw graphs of exponential functions, starting with y = e^x. It covers the behavior of the graph, including its y-intercept at (0,1), its approach to zero on the negative x-axis, and its rise to infinity on the positive x-axis. The tutorial then moves on to graphing a more complex function, y = 3e^(-2x) - 5, detailing the steps to find x and y intercepts, and the behavior of the graph as x approaches positive and negative infinity. The video concludes with a sketch of the graph, emphasizing the importance of understanding these concepts for graphing other exponential functions.

What is the general form of an exponential function?

• y = log(x)

• y = mx + b

• y = ax^2 + bx + c

• y = a^x

What is the y-intercept of the graph y = e^x?

• (1, 0)

• (1, 1)

• (0, 1)

• (0, 0)

As x becomes more negative in y = e^x, what does the graph approach?

• Zero

• One

• Infinity

• Negative infinity

What happens to the graph of y = e^x as x increases?

• It remains constant

• It approaches zero

• It decreases

• It increases indefinitely

In the function y = 3e^(-2x) - 5, what does the '-5' represent?

• Frequency

• Amplitude

• Horizontal shift

• Vertical shift

What is the first step in graphing y = 3e^(-2x) - 5?

• Calculate the slope

• Find the x-intercept

• Find the y-intercept

• Determine the asymptotes

How do you find the x-intercept of y = 3e^(-2x) - 5?

• Set y to zero and solve for x

• Find the integral

• Set x to zero and solve for y

• Find the derivative

What is the y-intercept of y = 3e^(-2x) - 5?

• (0, 0)

• (0, -5)

• (0, 3)

• (0, -2)

As x approaches infinity in y = 3e^(-2x) - 5, what does y approach?

• Three

• Infinity

• Negative five

• Zero

What happens to y = 3e^(-2x) - 5 as x approaches negative infinity?

• y approaches negative five

• y approaches zero

• y remains constant

• y approaches infinity