The figure below shows the graph of f g h and p Suppose fx

The figure below shows the graph of f, g, h and p. Suppose f(x) = z^2 (black graph). Define the function g using the function f. g(x) = f(x + 4) Define the function h using the function f. h(x) = f(x - 4)/2 +7 Define the function p using the function f. p(z) = f(x - 4)/4 +7 Whit is the function rule for p? p(z) = ________

Solution

let f(x)=x² then

(a).

since the original graph is shifted 4 units right, so

g(x)= (x-4)²

Hence g(x)=f(x-4)

(b)

Then to get the graph of h(x), first we shift f(x) 4 units right and then 7 units up. to get

h(x)= (x-4)² +7

Hence h(x)=f(x-4)+7

(c)

Again then to find the value of p(x), we stretch the graph in y direction with a scaling factor of 3. Hence

p(x)=3 (x-4)² +7

Hence p(x)=3f(x-4)+7

(d)

the funcion p(x) obtained by shifting the original curve f(x)=x² to 4 units right side and then shift 7 units upward and then stretch in y direction by a factor 3. Hence

p(x)=3 (x-4)² +7.