As you complete Check it Out, try to determine how the values a and b in the equation y = abx affect the shape and position of the corresponding graph.

Click here to go to The Exponential Function link to explore exponential functions. (Alternately, you can complete this activity using your graphing calculator.)

Complete the following questions to investigate the relationship of the equation y = abx to its graph.

Click here to check your answer

    1. Parameters are the constants in the equation of a function. Use the slider to set parameter b to 1.5. Then, set parameter a to each value shown in the chart on the next page. For each a-value, complete the chart as shown in the example. (Using your calculator, input the equation into Y1.)

Example:

Parameter a
Equation
Graph
y-intercept
3.5
y = 3.5(1.5)x
3.5
2
0.5
0.25

  1. Describe how the graph changes as the value of a decreases.

  2. How does the a-value relate to the y-intercept of the graph?

  3. Describe the shape of the exponential functions you sketched in 1.

  4. How does changing the a-value affect the shape of the graph?

  5. Describe the end behaviour of the exponential functions you sketched in 1.

  6. How does changing the a-value affect the end behaviour of the graphs?

  7. Set parameter a to 1.5. Then, set parameter b to each value shown in the chart below. For each b-value, complete the chart as shown in the example.

Parameter b
Equation
Graph
y-intercept
3.5
y = 1.5(3.5)x
1.5
2
0.5
0.25

  1. Describe how the graph changes as the value of b decreases.

  2. How does the b-value relate to the y-intercept of the graph?

  3. Describe the shape of the exponential functions you sketched in 8.

  4. How does changing the b-value affect the shape of the graph?

  5. Describe the end behaviour of the exponential functions you sketched in 8.

For b > 1

For 0 < b < 1

  1. How does changing the b-value affect the end behaviour of the graphs?