The function is defined by . What is the value of ?
For problems asking for the value of a function at a specific input, directly substitute the given number for , then simplify step by step. With absolute value functions, first replace , then evaluate the absolute value carefully (making the result nonnegative), and only after that do the multiplication and addition. This keeps sign errors from absolute value from costing you time and points.
Hints
Start by substituting
Replace with everywhere it appears in the expression .
Think about absolute value
What is the absolute value of ? Remember, absolute value represents distance from 0 and is always nonnegative.
Follow order of operations
After you find , multiply that result by 2, then add 3.
Desmos Guide
Enter the function and evaluate at -4
In Desmos, type g(x) = 2|x| + 3 (use the abs button or |x| for absolute value). Then, in a new line, type g(-4) and look at the output that Desmos gives; that number is the value of .
Step-by-step Explanation
Substitute the given input into the function
The function is defined as .
To find , replace with :
Evaluate the absolute value
Recall that the absolute value of a number is its distance from 0 on the number line, so it is always nonnegative.
So:
Substitute this into the expression:
Simplify the arithmetic
First multiply, then add:
Now add 3:
So the value of is 11.