Graphing Exponential Functions: Key Concepts and Techniques

Mr. Bergman introduces exponential functions, explaining basic exponent rules and graphing techniques. He discusses transformations, such as vertical and horizontal shifts, and changes in base. The lesson covers exponential growth and decay with practical examples, concluding with a personal note.

What happens to the value of 2 raised to a negative exponent?

• It becomes a fraction.

• It becomes a negative number.

• It becomes zero.

• It becomes an imaginary number.

What is the term for a line that a graph approaches but never touches?

• Asymptote

• Tangent

• Secant

• Intercept

How does the graph of f(x) = 2^x + 1 differ from the graph of f(x) = 2^x?

• It is shifted one unit up.

• It is shifted one unit to the right.

• It is shifted one unit down.

• It is shifted one unit to the left.

What happens to the graph of an exponential function when the base is changed from 2 to 3?

• The graph shifts to the left.

• The graph shifts to the right.

• The graph becomes less steep.

• The graph becomes steeper.

What is the effect of a horizontal shift on the graph of an exponential function?

• It changes the base of the function.

• It changes the steepness of the graph.

• It moves the graph left or right.

• It moves the graph up or down.

What is the result of multiplying a number by 1.02?

• A 2% decrease

• A 2% increase

• A 20% increase

• A 20% decrease

If a car's value depreciates by 15% each year, what is the multiplier used to calculate its value after one year?

• 1.85

• 1.15

• 0.85

• 0.15

What is the formula for calculating the final amount in exponential growth?

• A = P(1 - rt)

• A = P(1 + r)^t

• A = P(1 - r)^t

• A = P(1 + rt)

What is the range of the function f(x) = 2^x?

• (-∞, ∞)

• (0, ∞)

• (-∞, 0)

• (0, 1)

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

• 0

• 1

• 4

• 2