Question

Identify a possible graph for function $f$ given by
$f\left(x\right)={(x-2)}^3+1$

• A. graph a
• B. graph b
• C. graph c
• D. graph d

Answer 1

The correct option is D graph d

Let $y=(x-2{)}^3+1$

The graph of $f\left(x\right)$ in this example is the graph of $y=(x-2{)}^3+1$. It is easy to generate points on the graph.

Choose a value for the first coordinate, then evaluate $y$ at that number to find the second coordinate.

The several values for $x$ and the function $y$ evaluated at those numbers.

If $x=0$, then $y=(0-2{)}^3+1=-8+1=-7$implies the point is $(0,-7)$.

If $x=1$, then $y=(1-2{)}^3+1=-1+1=0$implies the point is $(1,0)$.

If $x=2$, then $y=(2-2{)}^3+1=0+1=1$implies the point is $(2,1)$.

Hence, the graph of the function is shown above.