How do you rewrite $$f(x) = 3 \times 2^{\frac{x}{2}}$$ in the form $$y = ab^x$$ ?

$$f(x) = 3 \times ig(\frac{\text{1}}{\text{2}}ig)^{x}$$ .

What does it mean for two exponential functions to be equivalent?

Two exponential functions are equivalent if they can be expressed in the same form $$y = ab^x$$ with the same base and initial value.

How do you find the initial value in an exponential function?

The initial value is represented by $$a$$ in the function $$y = ab^x$$ .

What is the significance of the base in an exponential function?

The base determines the rate of growth or decay of the function; if $$b > 1$$ , the function grows, and if $$0

How can you convert $$f(x) = 3 \times 2^{\frac{x}{2}}$$ to a different base?

You can express it as $$f(x) = 3 \times (2^{\frac{1}{2}})^x$$ .

What is the relationship between $$f(x) = a \times b^x$$ and its graph?

The graph of an exponential function is a smooth curve that either increases or decreases, depending on the base $$b$$ .

How do you determine if an exponential function is increasing or decreasing?

If the base $$b > 1$$ , the function is increasing; if $$0

Topic 2.4 - Exponential Function Manipulation Flashcards

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FLASHCARD QUESTION

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Define an exponential function.

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2.

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What is the general form of an exponential function?

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