A composite function feeds an expression into another function. When a new rule contains , use Desmos to evaluate the expression inside first. Then look for that input among the points given for , and apply anything outside last. You don't need the line's equation if a given point already supplies the output you need.
Hints
- Hint 1
In function notation, means put in for in the rule for . Find the whole input to first: what does give?
- Hint 2
A point on a function graph pairs an input with its output: means . Which given point has the input you found inside ?
- Hint 3
The is outside , so add it after you find 's output. What calculation uses the matching point's second coordinate?
Step-by-step
Match the inside input to a given point
Step 1Find the input to
To find , put in for inside . Type in Desmos. It shows , so . Here is the input, the number fed into , not yet the output of .
- Step 2
Read the matching output
A point on the graph of gives an input first and its output second. Since is on the line, . Use this point, not : its first coordinate matches the input you found.
- Step 3
Apply the outside addition
Replace with its output, . Type on a new Desmos line; it shows . So . Work inside first, then apply what lies outside it. Choice C.