Question 112·Medium·Algebra

Pick any two points from the table, such as $(0,-2)$ and $(2,4)$, and use the slope formula $m = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}$ to find the rate of change.

Once you know the slope, use $f(x) = mx + b$ and the fact that $f(0)$ is given in the table to find $b$. Then substitute $x = 3$ into your equation for $f(x)$.

Create a table in Desmos and enter the $x$-values 0, 2, 6 in the first column and the corresponding $f(x)$-values $-2$, 4, 16 in the second column. Below the table, type y1 ~ m x1 + b to perform a linear regression. Desmos will display an equation of the form $y = mx + b$ that best fits the points (it should match the exact line through them).

Once you know the equation of the line from your work or from Desmos (for example, $f(x) = 3x - 2$), type that expression with $x = 3$ into a new line, such as 3*3-2. The numerical result that Desmos outputs is the value of $f(3)$; use that value to choose the correct answer option.

A linear function has a constant rate of change (slope). Use any two points from the table, for example $(0,-2)$ and $(2,4)$.

Compute the slope $m$:

So the slope of the function is $3$. This same slope also works between $(2,4)$ and $(6,16)$, confirming the function is linear with slope $3$.

Use slope-intercept form for a linear function:

You already know $m = 3$. Use the point $(0,-2)$ from the table to find $b$:

So the equation of the function is

Now substitute $x = 3$ into the equation $f(x) = 3x - 2$:

Therefore, the value of $f(3)$ is $7$, which corresponds to answer choice B.