Math

QuestionIdentify the equation that represents an absolute value function from these options: f(x)=9f(x)=-9, f(x)=13xf(x)=\frac{1}{3 x}, f(x)=x3x2f(x)=x-3 x^{2}, f(x)=14x+43f(x)=\frac{-1}{4}|x+4|-3.

Studdy Solution

STEP 1

Assumptions1. We have four functions to consider f(x)=9f(x)=-9, f(x)=13xf(x)=\frac{1}{3 x}, f(x)=x3xf(x)=x-3 x^{}, and f(x)=14x+43f(x)=\frac{-1}{4}|x+4|-3. . We are looking for an absolute value function, which is a function that contains an absolute value operation.

STEP 2

An absolute value function is a function that contains an absolute value operation. The absolute value operation is represented by the symbol x|x|, where xx is the input to the function. The absolute value of a number is its distance from zero on the number line, regardless of direction.

STEP 3

Let's examine the first function f(x)=9f(x)=-9. This function does not contain an absolute value operation, so it is not an absolute value function.

STEP 4

Next, let's examine the second function f(x)=13xf(x)=\frac{1}{3 x}. This function also does not contain an absolute value operation, so it is not an absolute value function.

STEP 5

Now, let's examine the third function f(x)=x3x2f(x)=x-3 x^{2}. This function does not contain an absolute value operation, so it is not an absolute value function.

STEP 6

Finally, let's examine the fourth function f(x)=14x+43f(x)=\frac{-1}{4}|x+4|-3. This function does contain an absolute value operation, so it is an absolute value function.
The equation that represents an absolute value function is f(x)=14x+43f(x)=\frac{-1}{4}|x+4|-3.

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