suppose f(x)=x^2 and g(x)=(1/3X)^2. Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 1/3 units right.
B. The graph of g(x) is the graph of g(x) is the graph of f(x) horizontally stretched by a factor of 3.
C. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 3.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a factor of 3.

See picture attached to see comparison. The parent graph is black and the new graph is red. By adding 1/3 to the graph, the parabola becomes more compressed and wider. It is vertically compressed to become wider.

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parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-05-15T14:19:33+02:00

Answer:

B. The graph of g(x) is the graph of g(x) is the graph of f(x) horizontally stretched by a factor of 3.

Step-by-step explanation:

Horizontal shifting right by c units,

[tex](x,y)\rightarrow (x-c,y)[/tex]

Horizontally stretched by factor c.

[tex](x,y)\rightarrow (\frac{x}{c},y)[/tex]

Vertically stretched by factor c. ( where, 0< |c|<1 )

[tex](x,y)\rightarrow (x,cy)[/tex]

Horizontally compressed by a factor of c. ( where, |b| > 1 )

[tex](x,y)\rightarrow (cx,y)[/tex]

Here,

[tex]f(x) = x^2[/tex]

When f(x) is shifted 1/3 unit right,

Then, the transformed function is,

[tex]g(x) = (x-\frac{1}{3})^2[/tex]

When f(x) is stretched horizontally by the factor of 3,

Then, the transformed function is,

[tex]g(x)=(\frac{1}{3}x)^2[/tex]

When, f(x) vertically stretched by a factor of 3,

Then, the transformed function is,

[tex]g(x)=3(x)^2[/tex]

When, f(x) is horizontally compressed by a factor of 3,

Then, the transformed function is,

[tex]g(x)=(3x)^2[/tex]

Hence, option B is correct.