Question 649·Medium·Math

0 / 2000

x	$f(x)$
0	$-2$
2	$4$
6	$16$

Some values of the linear function $f$ are shown in the table above. What is the value of $f(3)$ ?

A table for a linear function has a constant change in output for each $1$ increase in input. Find that rate from two rows, then use a nearby row to reach the input you need. Desmos can calculate the rate and the new output. Don't halve an output merely because you halve its input; the function may not start at $0$ .

Hints

Hint 1
The slope is the change in output divided by the matching change in input. Compare the rows for $x=2$ and $x=6$ : how much does each column change? Keep the changes in the same order.
Hint 2
From $x=2$ to $x=3$ is one input step. A linear function changes by its slope on every such step, so add that change to the output at $x=2$ .

Step-by-step

Find the rate, then take one step
Step 1
Find the output change per input step
The slope is the output change divided by the input change. A linear function has the same slope between any two rows. From $x=2$ to $x=6$ , type $\frac{16-4}{6-2}$ in Desmos. It shows $3$ , so the output rises by $3$ for each increase of $1$ in $x$ .
Step 2
Move from the known output to the requested one
The table gives $f(2)=4$ , and $3-2=1$ input step. Type $4+3(3-2)$ on the next Desmos line; it shows $7$ . Don't halve $f(6)=16$ because $3$ is half of $6$ : the table shows the output at $x=0$ is not $0$ . So $f(3)=7$ . Choice B.

Question 649·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this