Question

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)?

Answer 1

Answer:

Vertically compressed by 1/9 not 3

Step-by-step explanation:

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.

Answer 2

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,

$(x,y)\rightarrow (x-c,y)$

Horizontally stretched by factor c.

$(x,y)\rightarrow (\frac{x}{c},y)$

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

$(x,y)\rightarrow (x,cy)$

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

$(x,y)\rightarrow (cx,y)$

Here,

$f(x) = x^2$

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

Then, the transformed function is,

$g(x) = (x-\frac{1}{3})^2$

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

Then, the transformed function is,

$g(x)=(\frac{1}{3}x)^2$

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

Then, the transformed function is,

$g(x)=3(x)^2$

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

Then, the transformed function is,

$g(x)=(3x)^2$

Hence, option B is correct.