Transform f(x)=x^2 to y=2f(-1/2(x+5))-3

[aisha]

if f(x)=x^2 write the equation for the transformed function y=2f(-1/2(x+5))-3

the answer was y=1/2(x+5)^(2)-3

How do u get this answer? What happened to the 2f? and the - in 1/2?

Also how would the new function be graphed? What would it look like?

 

[quasar987]

Here, 2f(-1/2(x+5))-3 does not mean 2 times f time -1/2(x+5) minus 3. It means, y is 2 times the function f(x)=x^2 where x is being replaced by the expression -1/2(x+5), minus 3.

 

[Doc Al]

if f(x)=x^2 write the equation for the transformed function y=2f(-1/2(x+5))-3

A less confusing way of writing it would be: f(g) = g^2. Now y = 2f(g) - 3, where g = -1/2(x+5). So: y = 2f(g) - 3 = 2g^2 - 3. You finish it by substituting for g.

 

[ComputerGeek]

A less confusing way of writing it would be: f(g) = g^2. Now y = 2f(g) - 3, where g = -1/2(x+5). So: y = 2f(g) - 3 = 2g^2 - 3. You finish it by substituting for g.

I hate Math textbooks that set the students up with badly written problem sets just to make them harder than they really are.

though in all fairness, this could have been a starred question in the problem set.

 

[James R]

if f(x)=x^2 write the equation for the transformed function y=2f(-1/2(x+5))-3

the answer was y=1/2(x+5)^(2)-3

The thing to realize about functional notation like f(x) is that x is a place holder. In other words, all of the following are equivalent definitions of the function f:

f(x) = x^2
f(y) = y^2
f(stuff) = (stuff)^2
f(_) = _^2

In your expression for y, we see f(-1/2(x+5))

Since f(anything) = anything^2, we get:

f(-1/2(x+5)) = (-1/2(x+5))^2 = 1/4(x+5)^2

Now y is another function, defined to be:

y(x) = 2x - 3

or

y(_) = 2 × _ - 3

We want y(f(-1/2(x+5))). Putting it all together:

y(f(-1/2(x+5))) = y(1/4(x+5)^2) = 2 [1/4(x+5)^2] - 3 = 1/2(x+5)^2 - 3

 

[aisha]

Thanks everyone esp James I totally get it now, but it is sort of complicated at first.