Question

1.Describe how the graph of y= x2 can be transformed to the graph of the given equation.
y = x2 - 14

Shift the graph of y = x2 right 14 units.
Shift the graph of y = x2 up 14 units.
Shift the graph of y = x2 left 14 units.
Shift the graph of y = x2 down 14 units.

Answer 1

2.Describe how the graph of y= x2 can be transformed to the graph of the given equation.
y = (x-14)2 - 9

Shift the graph of y = x2 down 14 units and then left 9 units.
Shift the graph of y = x2 right 14 units and then up 9 units.
Shift the graph of y = x2 right 14 units and then down 9 units.
Shift the graph of y = x2 left 14 units and then down 9 units.


3.Describe how to transform the graph of f into the graph of g.
f(x) = x4 and g(x) = -x4

Reflect the graph of f across the x-axis.
Shift the graph of f down 1 unit.
Reflect the graph of f across the x-axis and then reflect across the y-axis.
Reflect the graph of f across the y-axis.


4.The transformation from f to g represents a __________ stretch.
f(x) = and g(x) = 6

Note: Use all lowercase letters in your response.

5.Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x3 + 4 and g(x) =

Answer 2

In general, if you have y = x^2 and you add some number to it (say 5), then you are moving the graph up (5 units)

If you subtract a number from it (again say 5), you are shifting the graph down (5 units)

Answer 3

okay, thank you

Answer 4

what about for the last three?

Answer 5

you're welcome

Answer 6

I'll do 2 more, but you should really post each question individually (it will save space and draw in more people to help)

Answer 7

y = x^2 is your parent graph, which is your standard parabola (opening upward)

if you replace x with x-14, you are effectively moving the graph 14 units to the right (not left). Notice how when x = 0, then y = x^2 turns into y = 0. Then when x = 14, y = (x-14)^2 turns into y = 0. So that proves we have moved 14 units to the right

Answer 8

Finally, we're subtracting 9 from the whole thing. So we shift the whole graph down 9 units

Answer 9

making sense so far?

Answer 10

ish?

Answer 11

where are you stuck

Answer 12

okay i got it now, i had to reread what your saying.. i need help with 3 and 5, i understand the other ones now, (thanks to you)

Answer 13

If you have any function, and you stick a negative sign outside the entire function, then you are changing the y coordinates of the graph from negative to positive (or vice versa)

Answer 14

So say you start with y = x^2

The y coordinates are all positive on this graph

but if you stick a negative sign out front, you get y = -x^2 and that turns all the positive y coordinates negative

Answer 15

So what happens is that you get a reflection over the x axis

Answer 16

for instance, say you had these points that make up this parabola