Function transformation involves changing the form of a function
The function g(x) is 
The function is given as:
g(x) is an exponential function that passes through points (-2,2) and (-1,4).
An exponential function is represented as:
At point (-2,2), we have:
At point (-1,4), we have:
Divide both equations
Simplify
Apply law of indices
Rewrite as:
Substitute 2 for b in
This gives
Multiply both sides by 4
Substitute 8 for (a) and 2 for (b) in
Express as a function
Hence, the function g(x) is
Read more about exponential functions at:
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Answer: 
<u>Step-by-step explanation:</u>
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Answer:
angle x = 98
angle y = 82
angle z = 82
Step-by-step explanation:
angle y + 98 = 180; therefore, angle y = 82 degrees
angles z and y are alternate interior angles and are congruent (equal)
angle x is 98 degrees because angles x and y are same-side interior and their angles are supplementary (add up to 180 degrees)
Answer:
Arc AC = 90°
Step-by-step explanation:
Postulate:
The measure of an arc will ALWAYS be equal to the measure of the central angle of the circle.
The angle of arc AC is marked with a square.
That square mark means it is 90°.
So the arc would also measure 90°.
Cheers
By "which is an identity" they just mean "which trigonometric equation is true?"
What you have to do is take one of these and sort it out to an identity you know is true, or...
*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5 cscx = 5/3
cosx = 4/5 secx = 5/4
tanx = 4/3 cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!
Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.
Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)
Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 + 3/4)².
By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
