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12345 [234]
3 years ago
14

50 pts help! Function g is transformation of function f. What is the equation of function g?

Mathematics
1 answer:
pav-90 [236]3 years ago
6 0

Answer:

The transformations are a reflection across the x-axis and a vertical stretch by a factor of 3. This means that g(x)= −3f(x)

Transformations of Graphs

Many graphs can be formed from a known graph using graph transformations. Some of the most common transformations are below.  

• −f(x) is the graph of f(x),but reflected across the y axis.  

• f(−x)is the graph of f(x), but reflected across the x axis.  

• cf(x) is the graph of f(x), stretched vertically by a factor of c, if c>1or compressed vertically by a factor of c, if 0<c<1.

• cf(x) is the graph of f(x), compressed horizontally by a factor of 1c, if c>1 or stretched horizontally by a factor of 1c, if 0<c<1.

•  The graph of f(x)±c is the graph of f(x) shifted vertically up (for +) or down (for -) c units.  

• The graph of f(x±c) is the graph of f(x) shifted horizontally left (for +) or right (for -) c units.

Step-by-step explanation:

First, when examining the graphs of f and g notice that the graphs appear to be reflections of each other - but not quite perfectly. The graph of f goes up from left to right while the graph of g goes down from left to right. So there is a reflection across the x-axis.  

However, there is also some stretching that is occurring. The graph of both functions contains the point (1,0), but comparing some other points, the graph of f has (0,−1) while the graph of g has the point (0,3). With just a reflection, the graph of g would have (0,1), so it appears to be a vertical stretch by a factor of 3. Checking another point to confirm, the graph of f has a point near (−6,−2). A reflection across the x-axis would result in (−6,2) and a stretch by a factor of 3 would then make the point (−6,6), which matches the graph of g.

So, the transformations are a reflection across the x-axis and a vertical stretch by a factor of 3. This means that g(x)=−3f(x)g(x)=−3f(x)

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If f(x) = 3^2 + 10x and g(x) = 2x-4, find (f-g)(x).
Marat540 [252]

What we know:      

f(x)=3^2+10x\\g(x)=2x-4                

(Also, 3^2=9)

What we need to solve:

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3 years ago
Given sin theta= 6/11 and sec theta &lt; 0, find cos theta and tan theta.
bekas [8.4K]

Answer: option a.

Step-by-step explanation:

By definition, we know that:

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Substitute sin(\theta)=\frac{6}{11} into the first equation, solve for the cosine and simplify. Then, you obtain:

cos(\theta)=\±\sqrt{1-(\frac{6}{11})^2}\\\\cos(\theta)=\±\sqrt{\frac{85}{121}}\\\\ cos(\theta)=\±\frac{\sqrt{85}}{11}

As sec\theta then cos\theta:

cos(\theta)=-\frac{\sqrt{85}}{11}

Now we can find tan\theta:

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4 0
3 years ago
Read 2 more answers
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FrozenT [24]

Answer:

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Step-by-step explanation:

440 - 100 = 340

LCM of 440 and 340

440 = 2 × 2 × 2 × 5 × 11

340 = 2 × 2 × 5 × 17

LCM = 2 × 2 × 2 × 5 × 11 × 17

LCM = 7480

4 0
3 years ago
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