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## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 7

Lesson 17: Stretching functions

# Reflecting & compressing functions

Given the graphs of functions f and g, where g is the result of reflecting & compressing f by a factor of 3, Sal finds g(x) in terms of f(x).

## Want to join the conversation?

• Is f(-1/3x) not equal to -1/3f(x)?
• I'm pretty sure that when the -1/3 is placed within the brackets containing "x", it alters the "x" values. Alternatively, if it is like "-1/3f(x)" then the y-values are being changed. I'm not entirely sure what the difference would look like graphically, however, on a table, Khan noticed that the y-values were -1/3 of f(x), so he wrote -1/3f(x).

If you selected two x values and you came up with -1/3, then the answer would be f(-1/3x).

Hope this helped.
• At , how do you just eyeball it
and know that is 1/3? doesn't make any sense for me.. :(
• When he draws it he is looking at how far below the x axis the line is, and then he finds the corresponding points above the x axis and sketches it as he goes. Eyeballing it just means he didn't carefully mark the points and then draw a super accurate representation.
• Even though I am able to identify shifts in the exercise below, 1) I still don't understand the difference between reflections over x and y axes in terms of how they are written. 2) I have constantly had trouble with the difference between horizontal and vertical compression of functions, their identification, and how their notation works. Could someone help me with this?
• For the first step, when he draws the opposite of the line, flips it, is this how you must solve every problem? Because I can't figure out how to draw the opposite of lines on graphs. Is this something you must practice at?
• For every value of the curve f(x), its reflection has the negative, -f(x). Try it, with, say, y = x, and y = x^2, y = sqrt(x) x>0, y = .5x+1, etc.
• How do you determine how the original equation is altered on the graph?
• How are we supposed to know how much we reflect, or if we should reflect?
• In my experience, knowing where/if to reflect is mainly something you have to build an intuition for. What I like to do is to experiment with transformations in my head until (mentally) I have transformed the original function into the new function.
• May seem off-topic, but why doe Mr. Khan repeat himself so much? Especially at - ?
(1 vote)
• It could be because he is restating what he said earlier while writing it, just to make sure if you missed what he said the first time, you hear it again. He might also record his videos without editing or in one take, and (from personal experience) if you are talking for a while, you tend to develop a habit of repeating phrases, especially while thinking about what to say next.
• What's the different between the functions f(kx) and kf(x) (k is a real number)? Is f(kx) always equal to kf(x) or they just equal in some case?
(1 vote)
• I think I can guess that k is the coefficient in this case, correct? So with f(kx) it acts on and changes the input, or x values, whereas kf(x) acts on and changes the output, or y values. Hopefully this helps.