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sweet [91]
1 year ago
11

The functions f and g are graphed in the same rectangular coordinate system, shown to the right. If g is obtained from f through

a sequence of transformations, find an equation for gWhat is the equation for g?

Mathematics
1 answer:
german1 year ago
3 0

The first thing we notice is that the function is reflected. So we can start by reflecting it with respect to the x-axis.

We do this by adding a negative sign in the function:

\begin{gathered} f_0(x)=x^2 \\ f_1(x)=-f_0(x)=-x^2 \end{gathered}

Now, we have the function reflected, but in the wrong position. We can track its position by the vertex. It was originally at (0,0) and remains at (0,0) after the reflection.

But the final function have its vertex at (-5,0), so we have to translate the function 5 units to the left. we do this by adding 5 to the x in the function:

f_2(x)=f_1(x+5)=-(x+5)^2

Now, to check if there isn't any dilatation, we can check on other point in the graph to see if it checks out.

In the blue graph, we see the point (-3,-4), so let's input x = -3 and see if it checks out:

f_2(-3)=-(-3+5)^2=-(2)^2=-4

We got y = -4, so it checks out.

Thus, the answer is:

g(x)=-(x+5)^2

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HELP:
wel

Answer:

First you can find the rate of change to be 4.25. Then you can subtract 4.25 repeatedly until you get to an output with an input of zero. The initial value is the output when the input is zero. The initial value after subtracting 4.25 three times is 29.50. Because the inputs go by 2, the rate of change is half the difference of the outputs, or 4.25. Subtract 4.25 repeatedly 3 times to get to an output with an input of 0. Calculate 42.25 – (3 x 4.25).  The initial value is 29.50.

Hope this Helps!

6 0
3 years ago
(-4, -7) and (-6, 9) in slope-intercept form. Show work
BigorU [14]

Answer:

Equation of line in slope-intercept form is: y = -8x-39

Step-by-step explanation:

Given points are:

(-4, -7) and (-6, 9)

The slope-intercept form is given by the equation

y = mx+b

Here m is the slope of the line and b is the y-intercept.

m is found using the formula

m = \frac{y_2-y_1}{x_2-x_1}

Here

(x1,y1) = (-4-7)

(x2,y2) = (-6,9)

Putting the values in the formula

m = \frac{9+7}{-6+4} = \frac{16}{-2} = -8

Putting slope in general equation

y = -8x+b

Putting (-6,9) in the equation

9 = -8(-6)+b\\9 = 48+b\\b = 9-48\\b = -39

Putting the value of b we get

y = -8x-39

Hence,

Equation of line in slope-intercept form is: y = -8x-39

5 0
3 years ago
Work out the area of a circle with a radius 6.2cm, take n/pi to be 3.142 and give your answer to 2 decimal places.
s344n2d4d5 [400]

Answer:

Step-by-step explanation:

Area is pi times r squared.  I don't know how to write that on the keyboard.  Take your pi(3.142) times the radius(6.2)squared.  Pemdas tell us to do exponents first, so 6.2 squared is 38.44.  To square a number, just multiply it times itself.  So now, we have pi(3.142) times the squared radius(38.44).  So, 3.142X38.44=

120.778  Second place is seven followed by eight.  Round up.  120.78

3 0
3 years ago
The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distr
Tanya [424]

Complete Question

The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test H_o : p =  0.28 vs H a : p <  0.28when the sample has n 900 , and \^ p = 0.216 with SE=  0.01 . Find the value of the standardized z -test statistic. Round your answer to two decimal places.

Answer:

The value is  z =  -6.40

Step-by-step explanation:

Generally the standardized test statistics is mathematically represented as

     z =  \frac{\^ p  -  p }{ SE }

=>  z =  \frac{0.216  -  0.28 }{ 0.01  }

=>  z =  \frac{0.216  -  0.28 }{ 0.01  }

=>  z =  -6.40

4 0
2 years ago
WHATS THE ANSWER?? answer ASAP NO FILE AT ALL
dlinn [17]

Answer:

B

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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