What are the x-intercepts of the function $$f(x) = a \times b^x$$ ?

An exponential function of the form $$f(x) = a \times b^x$$ has no x-intercepts because it never crosses the x-axis.

How does the graph of $$f(x) = 2^x$$ compare to $$f(x) = 3^x$$ ?

The graph of $$f(x) = 3^x$$ grows faster than the graph of $$f(x) = 2^x$$ for large values of $$x$$ .

What effect does a negative exponent have on an exponential function?

A negative exponent in an exponential function indicates decay; for example, $$f(x) = a \times b^{-x}$$ represents a decreasing function.

What is the transformation of the graph of $$f(x) = 2^x$$ to obtain $$g(x) = 2^{x-3}$$ ?

The graph of $$g(x) = 2^{x-3}$$ is a horizontal shift of the graph of $$f(x) = 2^x$$ to the right by 3 units.

What is the transformation of the graph of $$f(x) = 2^x$$ to obtain $$h(x) = 2^x + 4$$ ?

The graph of $$h(x) = 2^x + 4$$ is a vertical shift of the graph of $$f(x) = 2^x$$ upward by 4 units.

What is the vertical asymptote of an exponential function?

The vertical asymptote of an exponential function is the line $$y = 0$$ , which the graph approaches but never touches.

How do you find the y-intercept of an exponential function?

The y-intercept of an exponential function $$f(x) = a \times b^x$$ is found by evaluating $$f(0) = a \times b^0 = a$$ .

What is the significance of the constant $$a$$ in the function $$f(x) = a \times b^x$$ ?

The constant $$a$$ represents the initial value or the y-intercept of the exponential function.

What is the effect of changing the base of an exponential function?

Changing the base of an exponential function affects the rate of growth or decay; larger bases result in faster growth.

Exponential Graphs and Transformations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the base of an exponential function?

Back

3.

FLASHCARD QUESTION

Front

What is the general shape of the graph of an exponential function with a base greater than 1?

Back

4.

FLASHCARD QUESTION

Front

What is the general shape of the graph of an exponential function with a base between 0 and 1?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the domain of an exponential function?

Back

7.

FLASHCARD QUESTION

Front

What is the range of an exponential function with a positive base?

Back

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