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mixer [17]
3 years ago
6

Use the graph below to answer the following questions.​

Mathematics
1 answer:
Maru [420]3 years ago
3 0

Answer:

  • a) 3
  • b) x = {-3, -2, 2}

Step-by-step explanation:

Refer to attached for points

a) f(-1) = 3 as per graph

b) f(x) = 6

We add horizontal line through point y=6 to find intersections with the graph

Take x-values of those points. The points are x = -3, x = -2, x = 2

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Given the function f(x) = x2 and k = 3, which of the following represents the graph becoming more narrow?
Bess [88]
Functions A and C and D are translations - this means that they are exactly the same shape as f(x), but are displaced on the axes. A translation in the y-direction by k units is represented by f(x) + k, and a translation in the x-direction by k units is represented by f(x - k). This can be summarised in column vector notation:

A translation of the graph y = f(x), by the vector \left[\begin{array}{ccc}a\\b\end{array}\right] results in the graph defined by y - b = f(x - a). This is done by replacing x with (x - a) and y with (y - b). Finally it is rearranged to make y the subject, as is often the convention: y = f(x - a) + b.

Since the graph needs to change shape, this requires a 'stretch'. A stretch is performed by multiplying x or y by a constant, which here is k.

To stretch in the x-direction by a factor n, replace x with (1/n)x. Similarly to stretch in the y-direction by a factor n, replace y with (1/n)y.

For example to stretch y = f(x) by factor n in the x-direction, it would become y = f((1/n)x).

A simple quadratic graph like y = x^2 behaves slightly differently to most other graphs, in that it can narrowed by a stretch in the x or y direction. This means that a more convenient option is to perform a stretch in the y direction, since the multiplier lies outside the function notation. The stretching factor is 3, so we replace y with (1/3)y:

(1/3)y = f(x)
y = 3f(x)

Since k = 3, this becomes

y = kf(x)

... and hence the correct answer is B
6 0
3 years ago
Read 2 more answers
4) Write the quadratic equation of the following in vertex form: vertex (-1,3) and passes through (1,-5)
Lilit [14]
You will have to set up a system of equations
4 0
3 years ago
Read 2 more answers
maria purchased a new jacket for 78.12. the orginal price of the jacket was discounted 20% and Maria had to pay 5% sales tax. wh
prohojiy [21]
20 percent of the discount minus 5 percent sales tax equals to 15 percent.
know calculate the 15 percentage out of 78,12 so x on 78,12 equals to 20 on 100 so 78,12 equals to 100 percent and x equals to 15 percent so 78,12 times 15 divided by 100 is 15 percent or the number you found discount and and sales tax combined know you substact 15 percent out of your original price.


7 0
3 years ago
I will gave brainestly
hammer [34]

Answer:

Hello !

The solutions are: -8 , -4 , 6

Hope this helps !

3 0
3 years ago
What is the reduced answer to 4/9 multiples by 4/5 equal
deff fn [24]
First, we know that when multiplying fractions, we multiply both the numerator and denominator.

so, in 4/9 • 4/5,
4•4 = 16, and
9•5 = 45

so, 4/9 • 4/5 = 16/45.
now, we’ll look for the Least Common Factor

factors are numbers that you can multiply together to = another number.
the LEAST common Factor is the # that is smallest that you can divide both numbers by, in an equation and get a whole number.

for instance, 3•3 and 1•9 are the only ways to get 9, so, the factors are 1, 3, 9

let’s look for the LCF in 16 and 45. -
if we find the ways to get 16, we have:
1•16, 2•8, and 4•4
so, the factors are 1, 2, 4, 8, and 16.
this is called FACTORING :)

the ways to get 45 are...
1•45, 3•15, and 5•9, so the FACTORS are
1, 3, 5, 9, 15, & 45.
- compare the factors of 16 & 45,
none of them are the same besides 1, and we know that dividing these numbers by 1 will not do anything.

because of this, we can not reduce 16/45, so the reduced answer to 4/9 • 4/5 = 16/45
4 0
3 years ago
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