Question

allow3. The graph of function g is shown below.(a) Describe the graph as a transformation of f(x) = va(b) Write the equation for g.(c) State the domain and range of g.(d) Solve f(x) = 7 algebraically and graphically

Answer 1

For a)

$f(x)=\sqrt[]{x}$

In this case, we have a shift up by 4 and a shift to right by 2 units

For the shift up we need to add 4 to the function

For the shift to the right, we need to subtract 2 to the x

b) the equation for g is

$g(x)=\sqrt{x-2}+4$

c)

the domain is the set of all the possible values x can have

In this case

$\: \lbrack2,\: \infty\: )$

the range is the set of all possible values that the function can have

In this case

$\: \lbrack4,\: \infty\: )$

d)

$f(x)=\sqrt[]{x}$

$\sqrt[]{x}=7$

We isolate the x

$x=7^2=49$

Also, it can be observed in the graph looking for the value of x when f(x)=7