Question 85·Easy·Linear Functions
The function is defined by . What is the value of ?
For questions asking for when a function rule like is given, immediately rewrite the expression replacing with the given number, then simplify step by step using order of operations. Be especially careful with signs: copy the plus or minus exactly as shown so you don’t accidentally add when you should subtract or ignore a term.
Hints
Interpret the notation
Ask yourself: what does mean in terms of the formula ? How do you use the 4?
Substitute correctly
Everywhere you see in , replace it with 4. Write that new expression down before simplifying.
Follow order of operations
After substituting 4 for , do the multiplication first, then handle the subtraction carefully.
Desmos Guide
Use Desmos to evaluate the function
In Desmos, type f(x)=3x-7 to define the function. On the next line, type f(4). Desmos will show a single numerical output next to f(4); that number is the value of .
Step-by-step Explanation
Understand what means
The expression means "the value of the function when ." Since , you find by replacing with in the expression .
Substitute into the function
Start with the definition of the function:
Now replace with :
First do the multiplication: , so
Simplify the result
Now subtract:
So the value of is , which corresponds to choice D.