6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

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Multiple Choice

Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=\left(\frac12\right)^{x}$

Exponential function, $f\left(4\right)=\frac{1}{16}$

Exponential function, $f\left(4\right)=-16$

Not an exponential function

Verified step by step guidance

Step 1: Understand the definition of an exponential function. An exponential function is of the form f(x) = a^x, where 'a' is a positive constant called the base, and 'x' is the exponent.

Step 2: Analyze the given function f(x) = (1/2)^x. Here, the base 'a' is 1/2, and the exponent is 'x'. This matches the form of an exponential function.

Step 3: Since the function is an exponential function, identify the base and the power. The base is 1/2, and the power is 'x'.

Step 4: To evaluate the function for x = 4, substitute 4 into the function: f(4) = (1/2)^4.

Step 5: Simplify the expression (1/2)^4 by multiplying 1/2 by itself four times: (1/2) * (1/2) * (1/2) * (1/2). This will give you the value of f(4).

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Introduction to Exponential Functions practice set

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Struggling with College Algebra?

Determine if the function is an exponential function. If so, identify the power & base, then evaluate for x=4x=4x=4 .f(x)=(12)xf\left(x\right)=\left(\frac12\right)^{x}f(x)=(21)x

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Introduction to Exponential Functions practice set

Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=\left(\frac12\right)^{x}$