Evaluating Exponential Functions

The video tutorial explains how to evaluate exponential functions using a given function f(x) = 5^(3-x). It covers two main problems: calculating 2 times f(3) and the product of f(1+x) and f(1-x). The instructor demonstrates the use of function notation, substitution, and exponential rules to solve these problems step-by-step. The video concludes with a summary and encouragement to practice similar problems.

What is the base of the exponential function given in the video?

• 5

• 2

• 3

• x

What does the expression 2 times f(3) represent?

• 2 times the value of f at x=3

• 2 plus the value of f at x=3

• 2 minus the value of f at x=3

• 2 divided by the value of f at x=3

What is the first step in solving Part A?

• Multiply by 2

• Divide by 2

• Add 3 to x

• Substitute x=3 in f(x)

What is the value of f(3) for the function f(x) = 5^(3-x)?

• 2

• 0

• 5

• 1

What is the result of 2 times f(3) for the given function?

• 5

• 3

• 2

• 1

What is the result of 5^0?

• 1

• 5

• 10

• 0

In Part B, what expression do we evaluate first?

• f(x-1)

• f(1-x)

• f(1+x)

• f(x+1)

What is the expression for f(1+x) in terms of the given function?

• 5^(3+x)

• 5^(3-(1+x))

• 5^(3-1-x)

• 5^(3-x)

What is the expression for f(1-x) in terms of the given function?

• 5^(3+x)

• 5^(3-(1-x))

• 5^(3-1+x)

• 5^(3-x)

What is the first step in solving Part B?

• Multiply the expressions

• Simplify the exponents

• Add the exponents

• Substitute x with 1+x