What is the y-intercept of an exponential function of the form $$f(x) = a \times b^x$$ ?

The y-intercept is the value of $$f(0)$$ , which equals $$a$$ .

If $$f(x) = 2(4)^x$$ , what is the initial value?

The initial value (y-intercept) is 2, which is the value of $$f(0)$$ .

What does the term 'initial value' refer to in exponential functions?

The initial value refers to the value of the function when $$x = 0$$ , which is the y-intercept.

What is the range of an exponential function?

The range of an exponential function is all positive real numbers, typically expressed as $$y > 0$$ .

How can you determine if a function is increasing or decreasing?

If the base of the exponential function is greater than 1, the function is increasing. If the base is between 0 and 1, the function is decreasing.

What is the significance of the constant 'n' in the function $$p(x) = n(1.15)^x$$ ?

The constant 'n' represents the initial value or starting amount of the function.

What does it mean for a function to have a horizontal asymptote?

A horizontal asymptote indicates that as $$x$$ approaches infinity or negative infinity, the function approaches a specific value, usually $$y = 0$$ .

What is the difference between exponential functions and polynomial functions?

Exponential functions have a variable in the exponent (e.g., $$b^x$$ ), while polynomial functions have variables raised to whole number powers (e.g., $$x^2$$ ).

How do you find the y-intercept of an exponential function given in the form $$f(x) = a \times b^x$$ ?

To find the y-intercept, substitute $$x = 0$$ into the function, resulting in $$f(0) = a \times b^0 = a$$ .

M1_Intro to Exponential Functions 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 does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is an asymptote in the context of exponential functions?

Back

5.

FLASHCARD QUESTION

Front

How do you identify an exponential function from a set of functions?

Back

6.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

7.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

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