Graphing Exponential Functions and Analyzing Their Properties

This lesson introduces graphing exponential functions, focusing on y = 3^x, y = (1/3)^x, y = 2^x, and y = (1/2)^x. It explains how to plot these functions, identify key features like y-intercepts and asymptotes, and determine if a function is exponential by examining changes in y-values. The lesson also covers the impact of additional constants on the graph's shape and position.

What is the value of y when x=0 for the function y=3^x?

• 0

• 1

• 3

• 9

What property do exponential functions exhibit when their base is greater than 1?

• They increase

• They oscillate

• They remain constant

• They decrease

What is the asymptote of the graph y=3^x?

• y=1

• y=0

• x=0

• x=1

For the function y=1/3^x, what happens to the y values as x increases?

• They increase

• They decrease

• They remain constant

• They become negative

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

• 2

• 1

• 4

• 0

How does adding a constant to an exponential function affect its graph?

• Shifts it upwards

• Makes it linear

• Shifts it downwards

• No effect

What is the range of the function y=3^x+1?

• y < 1

• y < 0

• y > 1

• y > 0

For the function y=1/3^x - 1, what is the range?

• y > 1

• y < 1

• y > -1

• y < -1

What indicates an exponential function in a table of values?

• Values are all positive

• Values multiply by a constant

• Values decrease by a constant

• Values add by a constant

What is the domain of all exponential functions discussed?

• All integers

• All positive numbers

• All negative numbers

• All real numbers