Question

HELP PLASE<3

Answer 1

Answer:

Option B is correct.

The point which lies on the new graph g(x) is, (-3, 7.5)

Step-by-step explanation:

For a base function f(x), a new function g(x) = cf(x) is vertically stretched by a factor c if c> 1.

Given the parent function: f(x) =|x|

Now, by vertically stretched definition,

A function f(x) is vertically stretched by a factor of 2.5 then; we have the new function or new graph i.e,

g(x) = 2.5 f(x) where c=2.5 > 1

therefore, g(x) =2.5|x|

We have to find which point lies on the new graph;

Option A:

(-4 , -4)

Here x = -4 and g(-4) = -4

$g(-4) = 2.5 |-4|$

$-4=2.5 \cdot 4=10$

-4 = 10 False.

Option B:

(-3 , 7.5)

g(x) = 2.5|x|

$g(-3) = 2.5 |-3|$

$7.5= 2.5 \cdot 3=7.5$

7.5 = 7.5 True.

Option C:

(-2 , 5.5)

$g(-2) = 2.5 |-2|$

$5.5 = 2.5 \cdot 2=5$

5.5 = 2 False.

Option D:

(-1 , -2.5)

$g(-1) = 2.5 |-1|$

$-2.5 = 2.5 \cdot 1=2.5$

-2.5 = 2.5 False

Therefore, from above you can see that the only point which is true for the new graph is, (-3 , 7.5)

Answer 2

The answer is B (-3, 7.5)