graph of the function

Question

what would be the graph of functions

F(X) = f(2x)-1
G(X)= 1-2f(x)

Answer 1

Hi Zakia,

 

My guess is that this question is expecting you to treat f(x) as some unknown parent function, and then describe the effect on the parent that the numbers 2 and -1 for F(x) have on the parent. Likewise for G(x) what effect do the 1 and -2 have on the parent.

 

For F(x) the 2 (inside the parentheses) causes a horizontal shrink by a factor of 2. The -1 causes a vertical shift (translation) down 1.

 

For G(x)the -2 in front of f(x) has the effect of a vertical stretch, but also reflects f(x) over the x-axis. After the vertical stretch and reflection the +1 causes a vertical shift up 1.

 

See: https://www.desmos.com/calculator/hojjmldhtk for an example. Change the rule for f(x) to get an idea. Change the values of 2, -2, 1, -1 to other numbers to see what is happening. You might want to look up horizontal shrink/stretch to get a better understanding.

Answer 2

It depends of f(x)