Question 221·Medium·Nonlinear Functions
Which table gives three values of and their corresponding values of for function ?
When a function rule is given and the answer choices are tables, quickly plug each listed x-value into the function to compute the exact outputs, using exponent rules like and . Write down or mentally track the three pairs, then match them directly to the choice; you can also use the pattern of an exponential function (multiply by a constant factor, not add a constant) to eliminate obviously linear or mis-scaled tables without fully calculating every value.
Hints
Use the function rule directly
Each row of the table should come from plugging the x-value in that column into . Focus on finding , , and .
Handle the exponent carefully
When you plug in a value for , make sure you first compute in the exponent of 3. For example, what exponent do you get when ?
Remember special exponent values
Recall that and . After you find , multiply that result by 18 to get .
Check for exponential patterns
For an exponential function with base 3, as increases by 1, the output should be multiplied by 3 each time, not just increased by a constant amount.
Desmos Guide
Enter the function
Type y = 18*3^(x-1) into Desmos so it graphs the function .
Use a table to see the values
Click the plus (+) icon, choose "Table," and in the x-column enter 0, 1, and 2. Read the corresponding y-values in the table, then choose the answer option whose row matches those three y-values.
Step-by-step Explanation
Understand what the table should show
The function is . A table of values just lists inputs and the corresponding outputs . So we need to compute , , and using this formula.
Compute
Substitute into the function:
.
A negative exponent means a reciprocal: . So
.
So the correct table must have .
Compute
Substitute into the function:
.
Any nonzero number to the zero power is 1, so .
Thus .
So the correct table must have and .
Compute and match the table
Now substitute :
.
So the three ordered pairs are , , and . The only answer choice whose table lists , , and is choice C.