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Rainbow [258]
3 years ago
12

Write an equation for a linear function whose graph has the given characteristics.

Mathematics
1 answer:
BaLLatris [955]3 years ago
5 0
G(x) = 6x + 2....the slope here is 6. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal slope, we flip the original slope and change the sign. So our perpendicular line will have a slope of -1/6. (see how I flipped 6 (or 6/1) and made it 1/6, then I changed the sign and made it -1/6)

y = mx + b
slope(m) = -1/6
(42,0)....x = 42 and y = 0
now we sub and find b, the y int
0 = -1/6(42) + b
0 = -7 + b
7 = b

so ur perpendicular equation is : y = -1/6x + 7....or f(x) = -1/6x + 7


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The graphs of g(x) has only one x-intercept and is an odd function. The points (0,0), (1,3), and (3,1) are on the graphs of g(x)
Eddi Din [679]

Using translation concepts, it is found that the new intercepts are given as follows:

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<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the function was shifted one unit right, hence the rule for the translated function is given by:

(x,y) -> (x + 1, y).

The y-intercept is given by f(0), hence for the shifted function it will be f(-1). We have that f(x) is an odd function and f(1) = 3, hence f(-1) = -f(1) = -3.

The x-intercept is given by x when f(x) = 0, hence:

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More can be learned about translation concepts at brainly.com/question/4521517

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6 0
1 year ago
What is the equation for this parabola (located above) in vertex form?
riadik2000 [5.3K]

Answer:

<u>f(x)=x²-2x-2</u>

Step-by-step explanation:

<em><u>f(x)=ax²+bx+c</u></em>

f(0)=-2 => c= -2

f(1)= -3=> a+b-2=-3; a+b=-1

f(2)= -2; 4a+2b-2=-2; 4a+2b=0; 2a+b=0

a+b=-1 and 2a+b=0

2a+b-(a+b)=0+1=> a=1

2+b=0=> b=-2

f(x)=x²-2x-2

6 0
3 years ago
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