Question 232·Easy·Nonlinear Functions
Which table gives three values of and their corresponding values of for the given function ?
For function-to-table questions, translate the function rule into operations (here: add 1, then take the square root) and quickly plug in the given x-values one by one. Write down each resulting f(x) and then scan the answer choices, eliminating any table that disagrees on even a single value—this is faster and more reliable than trying to reason about patterns in the tables alone.
Hints
Focus on what f(x) means
Rewrite in words: what two operations are you doing to to get ?
Try just one x-value first
Start with . Compute by plugging into . Which tables have the correct value for ?
Check all three x-values
After you know , also compute and . Only one table will match all three values at once.
Desmos Guide
Use Desmos to evaluate the function at specific x-values
In Desmos, type the three expressions sqrt(0+1), sqrt(3+1), and sqrt(8+1) (you can put them on separate lines). Note the three numerical results Desmos gives you, then select the table choice whose row matches those three values in order for .
Step-by-step Explanation
Understand the function rule
The function is defined as
This means: for any input , you first add to , then take the square root of that result.
Evaluate the function at each given x-value
We are given -values , , and .
- For :
- Inside the root:
- For :
- Inside the root:
- For :
- Inside the root:
Match these (x, f(x)) pairs to a table
We found the three input–output pairs:
- , , and .
Look through the answer choices for the table that has -row and -row . That table is the correct answer.