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## Integrated math 3

### Course: Integrated math 3>Unit 6

Lesson 4: Scaling functions

# Scaling functions vertically: examples

The function k⋅f(x) is a vertical scaling of f. See multiple examples of how we relate the two functions and their graphs, and determine the value of k.

## Want to join the conversation?

• It looks like a parabola to me, why isn't it f(x^2)?
• f(x) just represents the output of the function, not the contents of the function itself. Since it is a parabola, it will probably have a kx^2 term in it (where k is a constant), but the output would still be f(x).
• Why do we know the points (5,0) and (-5,0)? Shouldn't you apply the same logic to these points as to the first examples, and multiply the f(x) by 1/3?

If this question doesn't make sense, I'm not surprised. I suck at math.

HEEEEEEEEEEEEEEELP!
• Exactly on point !

We know the point (-5,0) and (5,0) because it is already defined in the graph. The original function passes through those points, and that's why we know them.

In addition, we can multiply f(x) by 1/3. Just remember f(x) concerns with only the output not the input.

^^ Just to clarify that I mean, refer to the same problem at

f(-5) = 0
0*1/3 = 0

f(-2) = 2
2 * 1/3 = 2/3

f(3) = -3
-3 * 1/3 = -1

f(5) = 0
0*1/3 = 0

hopefully this helps !
• okay, so i see a problem in this video:
the video says that its supposed to be minutes along, but my video ends at
What's wrong with my video
(by the way, i still earn 850 energy points, but if you haven't watched the entire video, you still don't get all the energy points), so what's wrong?
i hope i'm making sense, but if i'm not, please feel free to comment!
• When I watched it, both the video and the transcript show the , I never saw where it was . So you did not miss anything.
• In the 1st graph, since f(x) is multiplied by 1/3, shouldn't the y-intercept change as well?
• Think about it like this:
It looks like the y-intercept for f(x) is at y=0.
If the whole equation is being scaled by 1/3, then to find out what the y-intercept will be for g(x), we should multiply the y-intercept from f(x) by 1/3 to find the new y-intercept.
1/3*0=0, so the y-intercept stays the same for this graph.
Keep going!
• When he makes the second graph, doesn't he forget to translate it downward?
• He does not, I would recommend checking the question again
• Question: Why in the second graph do we multiply the whole function by 2 and not only the absolute value x-3?
• When you have a Problem in the form -
A*|x - B| + C
Then -
A = scale factor or multiplier (you need to find A*|x-B| so multiply |x-B| by A)
B = horizontal shift (if B is positive shift to the NEGATIVE direction and vice versa)
C = vertical shift (If C is positive shift to the positive direction and vice versa)

Note: This works for other kinds of functions as well, not just absolute value functions. For example, you could have also had a square root instead of the absolute value sign.

• the parabola y = x^2 is scaled vertically by a factor of 7. What is the equation of the new parabola.
You can see that for every value for x^2, the y coordinate becomes seven times larger.
x=1; y=1 After scaling x=1; y=7
x=2; y=4 '""" x=2; y=28
etc.
General formula y=cx^2, whereby c is the scaling factor (vertically)
(1 vote)
• Couldn't we assume that since it is an odd function and the original function hits the points at (-3, 3) and (3, -3) that it would be the same but 1/3 of the way instead of individually finding where 1/3rd of the point would be for each point unless finding if it's odd or even has no pertinence or it can't always by applied this way??