Download Questions from Lessons 2/23 to 2/27 Topics covered: Vertical

Questions from Lessons 2/23 to 2/27
Topics covered: Vertical Transformations, Horizontal Transformations, Simplifying
Radicals, Square Root Functions, Cube Root Functions
Vertical Transformations:
Q: Need explanation for 1
A: No problem. Given the transformation g(x) = 5f(x) + 1, we know that the original
function’s outputs will compress and add 1. To find g(4), first find f(4). Since f(4) =
3, substitute 3 into the rule. So, multiply 3 by 5, then add 1. This gives you 16.
Q: how do you create an equation for the function when the problem gives
you the x- and y- intercepts ? (number 4)
because I'm not sure how to get the outputs for f(x)
A: Since the points are x-intercepts and y-intercepts, we know that the y-values are
0 for the x-intercepts, and the x-values are 0 for the y-intercept. So, we know three
points in f(x). They are (-3,0), (5,0), and (0,4). Since the transformation is g(x) =
3f(x), this means that the y-values of the function should be multiplied by 3,
resulting in a compression of the function.
Now, since the y-values are the values being affected, (-3,0) and (5,0) do not move.
However, (0,4) becomes (0,12). This is why the answer is choice 2.
Q: if g(x)= 3f(x) would the y intercept move or is it just stretching verically?
question 4
A: See the above answer. Since it is a vertical transformation, only y-values are
affected.
Q: Can you explain 5ab please.
A: For part a, multiplying by 2 compresses the function (or makes it narrower,
whatever you want to say). For part b, everything moves up by two units.
Excellent questions! Next topic…
Horizontal Transformations:
Q: How would you make a transformation rule for a graph?
A: The best I can say for this is to observe closely how the graph has changed. There
is a wide range of answers for this. Here is an example…
If f(x) is your original function, and the transformed graph shows that it flipped over
the x-axis and moved 5 spaces to the left, the rule would be –f(x + 5). Basically, make
sure you know the rules given in class.
Q: I struggled with number 1. Could you please explain step-by-step how to
do it? I get confused with the x and y values and where to substitute.
A: There is no substitution here. You were not given a function rule, so this will not
be done algebraically. Since the transformation is g(x) = –f(x + 1) – 3, this means
the function reflects over the x-axis, moves down 3, and then left 1. Just do this with
each point from the graph and you’ll see how it looks.
Q: For 2a) Is there a reflection or not? Because I believe that there is not a
reflection. But in class, you said there could be a reflection for the model (I
think it was the model). So I am a bit confused and a bit worried that I got
the question wrong.
A: This could go either way. Some may say there was a reflection over the y-axis
then a translation up 3 units, while others may just say it translates 2 right then 3
up. Either way it works.
Q: What is the step-by-step process for putting the x values through the
transformation rule and obtaining the new values?
A: I’ll make an example…
Assume you have the function f(x) = 3x + 1. Let’s take one ordered pair from this
graph, (2,7). Now, assume you are given the transformation rule g(x) = f(-2x). This
means that you have to take the x-values from f(x), multiply them by -2, then apply
the new values to 3x + 1. So, (2,7) would become (2,-11), demonstrating that the
function reflected over the y-axis and compressed. Try it out!
Q: Some parts of it were confusing. For example, I couldn't easily identify
the flip over the y axis so that was the hard part(2b).
A: I get that. Sometimes a reflection is hard to see. But in the case of 2b, a reflection
didn’t necessarily take place. It was a possibility, but not the only one.
Q: For the x values when calculating the outputs using a table, is there a
specific way to get those numbers?
A: I think this can be answered similar to the question above about the step-by-step
process. Let me know if you need clarification.
Q: for b i noticed it shifted one to the left, but also reflected over the y-axis.
but they're two separate rules so i didn't know how to explain them.
A: Well, you just explained it! However, it actually shifted 3 to the left before being
reflected, so this might explain why you had trouble.
Overall, very good work with the questions on this topic. I know this homework was
hard, but I’d rather you guys see the difficult stuff so there aren’t any surprises. On
to the next topic!
Simplifying Radicals:
Q: What do you do when there is number on the outside of the square root
sign?
A: Multiply it by what is on the “outside” after simplifying the radical.
Q: How do you do it if there is a fraction radical? like in number 6? Thanks.
A: Treat it like you are multiplying by ¼ or dividing by 4. So, simplify √32 to 4√2,
then divide the 4’s. The answer is just √2.
Q: I get confused to where I have to put the square root symbol when I
create the factor tree.
A: Never drop the radical symbol unless you are actually taking the root of a
number. So for example, if you are simplifying √20, you would write √4 and √5
under it. Then, you can take the square root of 4, so you just write 2. But you keep
the radical with the 5 since you can’t break that down. So the answer would be 2√5.
Q: if your question were to be a perfect cube how would you put it in
simplest radical form?
A: It’s the same process but with cube roots. So if we were simplifying 3√24, we need
to find the largest cube root that fits into 24. So we’d break that down into 3√8 and
3√3. Then, 3√8 = 2. So, the answer would be 23√3.
Q: How would you solve numbers 5 and 6?
A: #6 was mentioned above. For #5, you are given 5√20. Ignore the 5 for now and
simplify √20. You get 2√5. Now, multiply the 2 that is on the outside of the radical
by the 5 that was there before, so you get 10√5 as an answer. But the question only
wants the number that is outside, so the answer is 10.
Q: Are you supposed to add the coefficients after you simplify the square
root? I'm pretty sure that's what you're supposed to do, but math can be
tricky sometimes.
A: Multiply!
Awesome… Next!
Square Root Functions:
Q: How many x and y do you for the function???
A: I’m sure this is asking how many coordinates to use when graphing. I say at least
4, maybe even 5. Remember, be strategic about which points you plot, too. Try to
keep whole numbers, and remember what the curve should look like.
Q: I did not know what question 31 and 34 meant about translating the
function. I also don't understand how to find the domain and range of the
functions
A: Translating means “how does it ‘move’”? Remember that if you see a value added
or subtracted within the radical, the function will move left or right. If you see a
value added or subtracted outside of the radical, the function will move up or down.
Domain is the set of x-values that the function contains, while range is the y-values.
In the function y = √x, the domain is x ≥ 0 since every x-value greater than or equal
to zero has an output. The range would be y ≥ 0 since the outputs start as low as
zero and go up from there.
Q: how to get domain and range? how to know when it is <,>, ≥, ≤.
A: See the above answer. However, you use < or > when the starting value is not
included in the set. Use ≤ or ≥ when the starting value is included. On a graph, a
point is not included when an open circle is drawn on it, and a point is included
when the circle is darkened.
I got a couple more questions about domain and range, so here’s an example…
Domain: x ≥ 1
Range: y ≥ 2
That’s it for that! I’ll be adding cube root functions within the next day or so. Keep
the questions coming everyone!
Cube Root Functions: (coming soon)
Q:
A: