QuestionFind the domain and range of the function $f(x)=|x-4|+3$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=|x-4|+3$ . We need to find the domain and range of this function

STEP 2

The domain of a function is the set of all possible input values (x-values) which will produce a valid output from a particular function. For this function, $f(x)=|x-4|+$ , we can plug in any real number for x, and the function will still be valid. Therefore, the domain is all real numbers, or $(-\infty, \infty)$ .

STEP 3

The range of a function is the set of all possible output values (y-values) that we can get from the function. To find the range of the function $f(x)=|x-|+3$ , we need to consider the properties of the absolute value function.

STEP 4

The absolute value of a number is always non-negative. That is, $|x-4|$ is always greater than or equal to0. Therefore, $|x-4|+3$ is always greater than or equal to3.

STEP 5

Therefore, the range of the function $f(x)=|x-4|+3$ is $f(x) \geq3$ .
The domain and range of the function $f(x)=|x-4|+3$ are domain $(-\infty, \infty)$ ; range $f(x) \geq3$ .

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