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 value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

answer: 1, 3 and 5 are correct

step-by-step explanation: