Exponential Functions and Their Properties

The video tutorial explains how to graph the function f(x) = 2^(3-x) by breaking it down into simpler components. The function is rewritten as 8/(2^x) by using exponent rules. The tutorial then compares the graph of 8/(2^x) to 1/(2^x), highlighting the transformation caused by multiplying by 8. The explanation focuses on understanding the qualitative shape of the graph rather than plotting exact points.

What is the initial function given in the video?

• f(x) = 2^(3-x)

• f(x) = 2^(x-3)

• f(x) = 3^(2-x)

• f(x) = 2^(x+3)

How is the function 2^(3-x) initially split?

• 2^3 - 2^(-x)

• 2^3 * 2^(-x)

• 2^3 * 2^x

• 2^3 + 2^x

What is the value of 2^3?

• 4

• 10

• 8

• 6

How can 2^(-x) be rewritten?

• 1/(2^(-x))

• 2^x

• 1/(2^x)

• 2^(-x)

What is the simplified form of the function 2^(3-x)?

• 8 * 2^x

• 8/(2^x)

• 2^x/8

• 8 + 2^x

What is the effect of a negative exponent in the function?

• It results in a negative value.

• It results in a reciprocal.

• It results in a positive exponent.

• It results in zero.

What is the base of the function f(x) = 1/(2^x)?

• 1/2

• 4

• 2

• 3

How does the graph of f(x) = 1/(2^x) behave?

• It decreases exponentially.

• It remains constant.

• It increases exponentially.

• It oscillates.

What effect does multiplying by 8 have on the graph of f(x) = 1/(2^x)?

• It compresses the graph vertically.

• It shifts the graph to the left.

• It shifts the graph to the right.

• It stretches the graph vertically.

Where does the graph of f(x) = 8/(2^x) pass through on the y-axis?

• 4

• 2

• 1

• 8