Question

help

Answer 1

try to compare what's going on in the function to the table

Answer 2

for example, y = x^2 - 5 looks like y = x^2 - c which means a shift down by c units

so what happens to the graph of x^2 to get x^2 - 5?

Answer 3

"f(x) - c is the graph of f(x) shifted down by c units"

"x^2 - 5 is the graph of ___ shifted down by __ units"

try filling in the blanks

Answer 4

f(x) 5

Answer 5

should be "x^2 shifted down by 5" but you're starting to get the idea ^^

Answer 6

try to apply a similar line of reasoning to y = -2x^2 using row 5 and row 7 of the table

Answer 7

using row 5: "the graph of -f(x) is the graph of f(x) reflected across the x-axis"

now compare this to what is in the problem

y = -x^2 is the graph of ___ reflected across the ___-axis

try and fill in the blanks

Answer 8

f(x) x

Answer 9

now, use row 7 to figure out how multiplying x^2 by 2 changes the function

Answer 10

umm its reflected?

Answer 11

oh okay its stretched

Answer 12

now let's put everything together

"the graph of y = -2x^2 is the graph of x^2 stretched vertically by a factor of __ and reflected across the __-axis"

try filling in the blanks

Answer 13

y axis and factor of 2?

Answer 14

I think :/

Answer 15

refer to our earlier statements

Answer 16

f(x) x^2

Answer 17

the factor is 2
the reflection is across x-axis

"the graph of y = -2x^2 is the graph of x^2 stretched vertically by a factor of 2 and reflected across the x-axis"

Answer 18

keep in mind your description should mention x^2 not just the generic f(x)

Answer 19

OH I think I understand a little now

Answer 20

now use row 4 to figure out what transformation is being applied to x^2 to get (x-5)^2

Answer 21

shift to the right?

Answer 22

@Vocaloid

Answer 23

Good but how many units is it being shifted?

Answer 24

5?

Answer 25

Excellent

See if you can work out d using the table

Answer 26

Sorry wwas on break, if you do not mind can we still continue ? =)

Answer 27

@563blackghost @Shadow

Answer 28

@Vocaloid

Answer 29

would D be a stretch?

Answer 30

@Vocaloid

Answer 31

well by -3

Answer 32

horizontal or vertical?

when you consider stretches and shrinks ignore the negative sign because we account for that with reflection

Answer 33

*** should be a shrink since it's inside the parentheses and its > 1

Answer 34

now, instead of the generic "a" look at your problem and see what number you would replace "a" with

Answer 35

3

Answer 36

good, now put everything together

y = (-3x)^2 is a horizontal shrink by a factor of 1/3

now consider the negative sign

Answer 37

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
good, now put everything together

y = (-3x)^2 is a horizontal shrink by a factor of 1/3

now consider the negative sign
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 38

so this would be the answer, or are we not done yet

Answer 39

"now consider the negative sign"

Answer 40

alright

Answer 41

add this statement to the answer and then you're done

Answer 42

so reflect f(3)

Answer 43

across the y-axis, yes

Answer 44

reflect f(x) not f(3)

Answer 45

f(3) is a point not a graph

Answer 46

okay so the overall answer would be y = (-3x)^2 is a horizontal shrink by a factor of 1/3. Reflect f(3) over the y-axis.

Answer 47

actually they use y not f(x) so let's write it as

"y = (-3x)^2 is a horizontal shrink of y = x^2 by a factor of 1/3 and a reflection of y across the y-axis" done

Answer 48

Reflection of f(3) over the y-axis.**

Answer 49

okay i sort of get it now

Answer 50

you just match up the problem with the table you gave right

Answer 51

yeah, but also think about what is happening to the graph and try to visualize the transformations

Answer 52

okay now lets try a

Answer 53

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
should be "x^2 shifted down by 5" but you're starting to get the idea ^^
\(\color{#0cbb34}{\text{End of Quote}}\)

a is "y shifted down 5 units"

Answer 54

would it be shift f(x) downward c units?

Answer 55

oh okay

Answer 56

that's the correct line in the table but they want you to describe what is happening in the function given in the problem not the generic f(x) and c

Answer 57

5 units are being shifted to the right?

Answer 58

be careful with the parentheses, since the -5 is not inside parentheses it is being applied to the whole function not just x, making it a shift down not right

Answer 59

oh okay

Answer 60

so if it would be in the parenthesis it would be right

Answer 61

right and we are on the second one

Answer 62

yeah it would have to be (x-5)^2 to be a shift right

Answer 63

sure

Answer 64

because it is being applied to the entire function

Answer 65

yes

Answer 66

okay so it is being shifted down 5 units?

Answer 67

yes

Answer 68

so the answer would be shifted down 5 units

Answer 69

yes

Answer 70

okay now for b

Answer 71

reflect f(x) in the y-axis?

Answer 72

that's part of it, there's one more transformation though (consider the 2 coefficient)

Answer 73

um shrink f(x) vertically by a factor of a

Answer 74

for stretches and shrinks you can disregard the negative sign when determining whether a > 1 or < 1

Answer 75

okay so stretch

Answer 76

good, so it stretches it by 2 vertically and reflects across the x-axis = ans

Answer 77

*meant to correct you earlier about the axis of reflection whoops

Answer 78

its alright

Answer 79

now for c it would be shift f(x) to the right c units

Answer 80

good, so instead of c it's 5

Answer 81

because everything falls inside the parenthesis

Answer 82

yup

Answer 83

shift f(x) to the right 5 units

Answer 84

good ^^ they use "y" instead of f(x) though so I would just replace f(x) with y

Answer 85

and there is no second transformation for this one right

Answer 86

nope that's it

Answer 87

thank you so much