Exponential Functions and Graph Behavior

The video tutorial explains how to graph the function f(x) = 2^(3-x). It begins by simplifying the function to 8/(2^x) using exponent rules. The instructor then discusses how to graph 1/(2^x) and adjust it for the factor of 8, resulting in a graph that passes through 8 instead of 1. The tutorial concludes with a qualitative analysis of the graph's general shape, emphasizing that the graphs are not exact but provide a general understanding of the function's behavior.

What is the first step in simplifying the function f(x) = 2^(3-x)?

• Multiply the exponents

• Add the exponents

• Split the function into 2^3 and 2^(-x)

• Divide the exponents

What is the value of 2^3?

• 6

• 10

• 8

• 4

How can 2^(-x) be rewritten?

• 2x

• x^2

• 1/(2^x)

• 2^x

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

• 8 * 2^x

• 2^(3x)

• 2^x/8

• 8/(2^x)

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

• 1/2

• 3

• 2

• 1/3

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

• It decreases exponentially

• It oscillates

• It increases exponentially

• It remains constant

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

• It shifts the graph to the right

• It shifts the graph to the left

• It stretches the graph vertically

• It compresses the graph vertically

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

• 8

• 2

• 4

• 1

What is the main focus of the final section?

• Calculating precise values

• Memorizing formulas

• Qualitative understanding of graph shapes

• Exact plotting of points

Why are the graphs described as qualitative?

• They are based on numerical calculations

• They focus on the general shape rather than exact points

• They are plotted using software

• They are drawn with exact precision