Question 163·Easy·Nonlinear Functions
The function is defined by . What is the value of ?
For function-evaluation questions, write the function, substitute the given x-value carefully (especially minding negative signs), and then follow the order of operations step by step: simplify inside parentheses, then apply absolute value (or exponents), and finally add or subtract outside. For absolute value, first combine everything inside the bars into a single number, then make it nonnegative, which helps avoid common sign mistakes under time pressure.
Hints
Start by substituting
Take the function and plug in wherever you see . Write out explicitly before simplifying.
Be careful with negative numbers
When you substitute , you will get inside the absolute value. What is ?
Remember what absolute value does
After you simplify inside the bars to get a single number, apply absolute value (which makes the result nonnegative), and then add 2 at the end.
Desmos Guide
Evaluate the expression directly in Desmos
In Desmos, type abs(-3-5)+2 (this represents ) into an expression line. The numeric output that Desmos shows is the value of .
Step-by-step Explanation
Substitute the given x-value into the function
The function is defined as .
To find , replace with :
Now we need to simplify the expression inside the absolute value.
Simplify inside the absolute value
Compute :
So the expression becomes:
Now evaluate the absolute value.
Evaluate the absolute value and finish the calculation
The absolute value of a number is its distance from 0, so it is always nonnegative. Thus:
Substitute this back into the expression:
So the value of is 10.