Suppose f(x) = x2 and g(x) = 7x2. 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) vertically stretched by a factor of 7.
b. the graph of g(x) is the graph of f(x) shifted 7 units up.
c. the graph of g(x) is the graph of f(x) horizontally stretched by a factor of 7.
d. the graph of g(x) is the graph of f(x) vertically compressed by a factor of 7.

Therefore, The correct option is A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 7.

Step-by-step explanation:

For better explanation of the solution see the attached graphs of both the given functions :

The function f(x) is given to be : f(x) = x²

This is an equation of parabola open vertically upwards

The function of g(x) is given to be : g(x) = 7x²

This is also equation of the parabola open vertically upwards

Now, g(x) = 7x²

⇒ g(x) = 7 × x²

⇒ g(x) = 7 × f(x)

So, the graph of the function g(x) is vertically stretched by the factor of 7 as compared to that of the graph of the function f(x)

Therefore, The correct option is A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 7.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0