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Temka [501]
3 years ago
10

Given the function f(x) = x2 and k = 3, which of the following represents the graph becoming more narrow?

Mathematics
2 answers:
Bess [88]3 years ago
6 0
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
otez555 [7]3 years ago
3 0

Answer:

kf(x)

Step-by-step explanation:

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(a) The proportion of accidents that occur up to mile 1.2 of the path is the area under the density curve between 0 miles and 1.
inn [45]

Answer:

the area would be 0.4 or 40%

Step-by-step explanation:

The computation of the area is given below:

But before that the level of the density is

The density level is

=  1 ÷ (3 - 0)

= 1 ÷ 3

Area from 0 miles to 1.2 miles

= (1 ÷ 3) × (1.2 - 0)

= 0.4 or 40 %

Hence, the area would be 0.4 or 40%

the same is considered and relevant too

4 0
3 years ago
Please help with this im super lost and confused
postnew [5]

Answer:

D) C': ( -3, -2), D': ( -4, 1), E': ( -1, -2)

Step-by-step explanation:

Formula for this equation:

(x - 5, y - 3)

C:

(2, 1)

(x - 5, y - 3)

C': ( -3, -2)

E:

(4, 1)

(x - 5, y - 3)

E': ( -1, -2)

D:

(1, 4)

(x - 5, y - 3)

D': ( -4, 1)

3 0
3 years ago
If f is a function, then f(3x)=3f(x)
Delvig [45]
This is false.
The f(3x) means you are multiplying the input 'x' by 3 before plugging into the equation.
3f(x) means you are going to multiply your answer (output) by 3 after you've plugged the input value in and gotten the output.
7 0
3 years ago
PLEASE HELP 100 POINTS 100 100 100 PLEASSSSE
Oksi-84 [34.3K]

Answer:

b

Step-by-step explanation:

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