Question

A student says that the graph of the equation y = 3(x + 8) is the same as the graph of y = 3x, only translated upwards by 8 units. Do you agree? Why or why not?
A.S.A.P. I HAVE TO TURN THIS IN AT 10:30 HURRY PLEASE :)

Answer 1

Given:

A student says that the graph of the equation $y = 3(x + 8)$ is the same as the graph of $y = 3x$, only translated upwards by 8 units.

To find:

Whether the student is correct or not.

Solution:

Initial equation is

$y=3x$

$f(x)=3x$

Equation of after transformation is

$y=3(x+8)$

$g(x)=3(x+8)$

Now,

$g(x)=f(x+8)$      ...(i)

The translation is defined as

$g(x)=f(x+a)+b$        ...(ii)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (i) and (ii), we get

$a=8\text{ and }b=0$

Therefore, the graph of $y=3x$ translated left by 8 units. Hence, the student is wrong.