Question

how is the graph y=f(x)=│x│ transformed in order to change into the graph of g(x)=-2│x-5│
A.the graph is stretched vertically by a factor of 2
B.the graph is reflected about the x-axis
C.the graph is shifted horizionally 5 units to the right
D.the graph is shifted horizionally 5 units to the left
E.the graph is stretched vertically by a factor 1/2


Select all correct answer

Answer 1

f(x) ---> f(x - a) is a stretch of a units to the right

if you google 'transformation of graphs' you'll get a list of transformations

Answer 2

"Select \(all\) correct answer".
:)

Answer 3

@cwrw238 gave you one of them,
f(x) -> f(x-a) is a translation of "a" units to the right.

Here are some other ones:
f(x) -> -f(x) means a reflection about the x-axis.
f(x) -> k f(x) means a vertical stretch of factor k, if k>1, or
a vertical compression of factor, k if k<1.
that's all you'd need to finish making choices for this question.

Answer 4

ooops - sorry i overlooked the -2

as mathmate said there are a total of 3 transformations

Answer 5

let f(x)=x x<0
x^2 x>0
Then f(-2)-f(2) equals
A.-6
B.4
C.0
D.-2
E.-4

Answer 6

i got the last one i need help with the next one

Answer 7

note that for f(-2) x< 0
and for f(2) x > 0

Answer 8

ok

Answer 9

can u help me figure out the answer

Answer 10

f(x) = x if x < 0
so for f(-2):- f(-2) = 2

can you figure out the value of f(2) in a similar fashion?

Answer 11

so its -4

Answer 12

\(f(x)=x^2\) for x>0
so for x=2, x>0, so \(f(2)=2^2=4\)
Can you now put everything together to calculate
\(f(-2)-f(2)\)?