Given the functions f(x)= 1/x−4 +3 and g(x)=1/x+1 +6 .
2 answers:
ANSWER
The graph shifts 5 units left and 3 units up.
EXPLANATION
The given functions are:
and
We want to transform f(x) so that, it coincide with the g(x).
The required transformation is
Let us see why this works.
The transformation f(x+5)+3 will shift f(x) 5 units left and 3 units up.
The third choice is correct.
<u>Answer with step-by-step explanation:</u>
We are given a function which is to be transformed to another function
.
We are to determine whether which statement describes the transformation of the graph of function f onto the graph of function g.
Therefore, the correct answer option is: The graph shifts 5 units right and 3 units up.
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ANSWER
EXPLANATION
It was given that ∆CDE is an isosceles triangle.
The length of the sides are given in terms of x as follows.
It was also given that, angle D is congruent to angle E.
This implies that, side CD and CE are equal.
Thus,
In terms of x, we have;
We group like terms to get,
Divide both sides by 12 to get,
The length of the sides are;
EXPLANATION
It was given that ∆CDE is an isosceles triangle.
The length of the sides are given in terms of x as follows.
It was also given that, angle D is congruent to angle E.
This implies that, side CD and CE are equal.
Thus,
In terms of x, we have;
We group like terms to get,
Divide both sides by 12 to get,
The length of the sides are;
I'll do Problem 8 to get you started
a = 4 and c = 7 are the two given sides
Use these values in the pythagorean theorem to find side b
With respect to reference angle A, we have:
- opposite side = a = 4
- adjacent side = b =
- hypotenuse = c = 7
Now let's compute the 6 trig ratios for the angle A.
We'll start with the sine ratio which is opposite over hypotenuse.
Then cosine which is adjacent over hypotenuse
Tangent is the ratio of opposite over adjacent
Rationalizing the denominator may be optional, so I would ask your teacher for clarification.
So far we've taken care of 3 trig functions. The remaining 3 are reciprocals of the ones mentioned so far.
- cosecant, abbreviated as csc, is the reciprocal of sine
- secant, abbreviated as sec, is the reciprocal of cosine
- cotangent, abbreviated as cot, is the reciprocal of tangent
So we'll flip the fraction of each like so:
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Summary:
The missing side is
The 6 trig functions have these results
Rationalizing the denominator may be optional, but I would ask your teacher to be sure.