Exponential Graphs and Transformations

The video tutorial covers the domain and range of exponential graphs, explaining that the domain includes all real numbers while the range is determined by the asymptote. It provides examples to illustrate these concepts. The video also discusses the lack of symmetry in exponential graphs and the presence of asymptotes. Additionally, it explains how to perform reflections and translations on these graphs, including how to modify equations accordingly.

What is the domain of an exponential graph?

• All real numbers

• Only integers

• All negative numbers

• All positive numbers

In which direction does the domain of an exponential graph extend?

• Only to the right

• Neither direction

• Only to the left

• Both left and right

What is the range of an exponential graph with an asymptote at y=1?

• [1, ∞)

• (1, ∞)

• [0, ∞)

• (0, ∞)

Why can't the range of an exponential graph include its asymptote?

• Because it goes below the asymptote

• Because it is a vertical line

• Because it never reaches the asymptote

• Because it is undefined at the asymptote

What is the range of an exponential graph with a highest value of 2?

• (-∞, 2)

• (-∞, 2]

• (2, ∞)

• [2, ∞)

What is the domain of an exponential graph that has been moved one place up?

• All real numbers

• All negative numbers

• All positive numbers

• Only integers

Do exponential graphs have axes of symmetry?

• Depends on the graph

• Only sometimes

• No, never

• Yes, always

What is an asymptote in the context of exponential graphs?

• A line the graph approaches but never touches

• A point where the graph intersects the axis

• A line the graph crosses

• A point of symmetry

What is the equation of an exponential graph that has been moved one place up?

• y = x

• y = x + 1

• y = 1

• y = 0

What happens to the x-values when an exponential graph is reflected over the y-axis?

• They double

• They become negative

• They become positive

• They remain the same