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The graph of f(x) = |x| has been stretched by a factor of 2.5. If no other transformations of the function have occurred, which point lies on the new graph?


A( –4, –4)

B(–3, 7.5)

C( –2, 5.5)

D.( –1, –2.5)

Verified Answer :

The answer is B (-3, 7.5)

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)



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