Exploring Graphs of Exponential Functions

This video tutorial covers graphing exponential functions, starting with a review of input/output tables. It demonstrates graphing y = 2^x and compares linear and exponential growth. The tutorial also explores graphing with fractional bases, such as f(x) = 4*(1/2)^x, highlighting exponential decay. The video concludes with a practice example for viewers to try on their own.

What is the output when x = 0 for the function y = 2^x?

• 4

• 2

• 0

• 1

What does the graph of f(x) = 2^x look like?

• Parabola

• Hyperbola

• Straight line

• Exponential curve

How does the value of y change from x = 0 to x = 1 in the function f(x) = 2^x?

• Remains the same

• Doubles

• Increases by 2

• Increases by 1

What is the slope of the line y = 2x?

• 1

• 2

• 0.5

• 4

How does the output of f(x) = 2^x change as x increases?

• Decreases

• Increases exponentially

• Increases linearly

• Remains constant

What happens to the values of f(x) = 4 * (1/2)^x as x increases?

• Becomes negative

• Increases

• Decreases

• Remains constant

What is the value of f(x) when x = -1 for the function f(x) = 4 * (1/2)^x?

• 8

• 16

• 2

• 4

What is the behavior of the graph for f(x) = 4 * (1/2)^x as x moves to the right?

• Remains flat

• Oscillates

• Falls quickly then slows

• Rises quickly

For the function f(x) = 4 * (1/2)^x, what does the base of the exponent indicate about the graph's direction?

• It will oscillate

• It will fall

• It will remain constant

• It will rise

What general rule can be derived about exponential functions with a base between 0 and 1?

• They remain constant

• They rise then fall

• They fall as x increases

• They oscillate