6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

Struggling with College Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=\left(-2\right)^{x}$

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

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 and 'x' is the exponent.

Step 2: Analyze the given function f(x) = (-2)^x. Here, the base 'a' is -2, which is negative.

Step 3: Recall that for a function to be considered exponential, the base must be a positive real number. Since -2 is negative, this function does not meet the criteria for an exponential function.

Step 4: Evaluate the function at x = 4 to see if it behaves like an exponential function. Calculate f(4) = (-2)^4.

Step 5: Since the base is negative, the function does not consistently produce real number outputs for all real x, confirming it is not an exponential function.