Answer:
g (x) = 2 ^ (x + 2)
Step-by-step explanation:
For this case the transformation of f (x) is given by
g (x) = 2 ^ (x + 2)
To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)
For (-2,1)
g (-2) = 2 ^ ( -2 + 2)
g(-2)=1
For (-1,2)
g (-1) = 2 ^ ( -1+ 2)
g(-1)=2
For (0,4)
g (0) = 2 ^ ( 0+ 2)
g(0)=4
Here's what you have to keep saying to yourself until it carves a new
groove into your brain and you don't have to think about it any more:
<em> " log(x) = the power that 10 must be raised to </em>
<em> in order to wind up with 'x'. "</em>
You said 2.36 = -log(x)
Multiply each side by -1 : log(x) = -2.36
Now translate it into the mantra:
<em> The power that 10 must be raised to </em>
<em> in order to wind up with 'x' is -2.36 .</em>
Do you see what that means ? ! ?
If the power that 10 must be raised to in order to wind up with 'x'
is -2.36, then all you have to do to find 'x' is raise 10 to the power
of -2.36 ! You can do that with about 4 clicks on your calculator.
10^(-2.36) = <em>0.004365...</em> (rounded)
And if you don't quite believe it, it's even easier to check it.
Punch " 0.004365 " into your calculator, and then touch the
" 10^x " key, and something very close to -2.36 will pop up
right there, before your wondrous eyes.
10x+14>-230
-14 -14
10x>244
/10 /10
x>24.4
The basic form of linear function is
y=ax+b
For finding the slope, use the slope formula.
(4-2)/(-2+1)= 2/-1=-2
We first found a which is -2.
Then insert any point to find the value of b. In this case, I will insert (1,-2).
-2=-2+b
b=-2+2=0
The linear graph is y=-2x