help determining an equation for g(x) in terms of f(x). (Transformations)

M

Madtemper

New member
Joined
Feb 18, 2021
Messages
4
A3007BF9-97ED-46F6-BAD0-02E9DF4EA571.jpeg
I have been having a difficult time trying to find the equation for g(x). I had picked out a few points from both functions, but the transformations were not apparent to me. Some guidance/help would be great!
 
g(x) has a slope of -1/2 and a y-intercept of 2. At this point you can just write down the equation of g(x).
f(x) has a slope of -3 and a y-intercept of 2. At this point you can just write down the equation of f(x).

Can you please do that and we can go from there.
 
Jomo said:
g(x) has a slope of -1/2 and a y-intercept of 2. At this point you can just write down the equation of g(x).
f(x) has a slope of -3 and a y-intercept of 2. At this point you can just write down the equation of f(x).

Can you please do that and we can go from there.
Click to expand...
Yes, I figured the equation for f(x) is y=3x+2. I guess in terms of just y=x, the equation for g(x) is y=-1/2x+2 but I assumed that this equation is irrelevant as it is not in terms of f(x).
 
Last edited:
Madtemper said:
Yes, I figured the equation for f(x) is y=3x+2. I guess in terms of just y=x, the equation for g(x) is y=-1/2x+2 but I assumed that this equation is irrelevant as it is not in terms of f(x).
Click to expand...
g(x) = -1/2 * x +2 = -1/6 *(3*x +2) + 7/3 = - f(x) * 1/6 +7/3..........corrected
 
Last edited by a moderator:
Madtemper said:
View attachment 25174
I have been having a difficult time trying to find the equation for g(x). I had picked out a few points from both functions, but the transformations were not apparent to me. Some guidance/help would be great!
Click to expand...
Assuming you're supposed to use transformations to do this (which does seem unnatural, since you can just find the equations of both functions), you might look at their slopes and use their ratio as your vertical stretch factor (which will technically include a reflection). Then you might first shift f by an appropriate amount so that the two lines intersect on the x-axis, and then apply the stretch you worked out. Those two transformations should to it. But there will be many other ways as well.
 
Madtemper said:
Yes, I figured the equation for f(x) is y=3x+2. I guess in terms of just y=x, the equation for g(x) is y=-1/2x+2 but I assumed that this equation is irrelevant as it is not in terms of f(x).
Click to expand...
Now YOU have to write g(x) in terms of f(x)

For example, suppose it turned out that g(x) = 4x+6. YOU need to realize that g(x) = 4x+6 = 2(x+3) = 2f(x). Is this clear? No matter what g(x) turned out to be it would NOT have f(x) in it unless you put there after seeing what g(x) equaled.

Also, where did y=x come from?????
 
Subhotosh Khan said:
g(x) = -1/2 * x +2 = -1/6 *(3*x +2) + 5/3 = - f(x) * 1/6 +5/3
Click to expand...
Madtemper said:
Could you please elaborate and clarify a bit on what you had done? Where did the -1/6 and 5/3 come from?
Thanks!
Click to expand...

What constant would you multiply 3x by to get -1/2 x? Answer -1/6. Now -1/6(3x+2) = -1/2x - 1/3. So you have the -1/2x which is good. Now you need the constant to be 2. The constant right now is -1/3. Well what do you add to -1/3 to get to 2? Hint: The answer is not 5/3 as Subhotosh said.
 

Jomo said:
What constant would you multiply 3x by to get -1/2 x? Answer -1/6. Now -1/6(3x+2) = -1/2x - 1/3. So you have the -1/2x which is good. Now you need the constant to be 2. The constant right now is -1/3. Well what do you add to -1/3 to get to 2? Hint: The answer is not 5/3 as Subhotosh said.
Click to expand...
You would add 2.333... to -1/3 to get to 2.
 
You must log in or register to reply here.
Top