Question

t	0	1	2	3
f(t)	-1	1	3	5

The table gives values of the function $f$ for several values of $t$. If the graph of $f$ is a line, which of the following defines $f\left(t\right)$?

• A. $f\left(t\right)$ $=t-1$
• B. $f\left(t\right)$ $=t+1$
• C. $f\left(t\right)$ $=2t+1$
• D. $f\left(t\right)$ $=2t-1$
• E. $f\left(t\right)$ $=1-2t$

Answer 1

The correct option is D $f\left(t\right)$ $=2t-1$

Let $x$ represents $t$ and $y$ represent $f\left(t\right)$

From given table coordinate $A(0,-1)$ and $B(1,1)$ and $C(2,3)$ and $D(3,5)$

Equation of line from point $A(0,-1)$ and $B(1,1)$

$y+1=\frac{1+1}{1-0}\left(x\right)$

$y+1=\frac{2}{1}\left(x\right)$

$y+1=2x$

$y=2x-1$

Hence

$f\left(t\right)=2t-1$