The point ~11,12) is on the graph of y = f(c)_ A point on the graph ofy = g(r) where g(k) f(c)point on the graph ofy = g(z) where g(t) f(z)A point on the graph of y...

Suppose that $g(x)=4^{x}+2$ (a) What is $g(-1) ?$ What is the corresponding point on the graph of $g$ ? (b) If $g(x)=66,$ what is $x ?$ What is the corresponding point on the graph of $g$ ?

This is for a were asked to find G evaluated at negative one. That was before the start of negative 12 That's 1/4 was, too, which is equal to well to is, hates over four. So we have 9/4 and now report being we have. If G of X is equal to 66 what is? That's what we have that D of X is for plus two. Well, it's the drop to humble side. So we get 64 because you could afford to our ex anything, right? Six before with the base of a bullet that is 40 part three. You could afford a car. This is the of the same base you see, There are powers are equal, that is X must be equal to three.

For part A. If we wanted to find G of negative one, we called negative one in for Accent of the Function. So it's four to the negative first plus two, four to the negative. First it was 1/4 was 1/4 to the first cost to which is to in the fourth, which is 9/4. And so the point on the graph it corresponded. This would be an input of negative one is an output of 9/4. Prepare be What if g of X for 66? Well, we would have G of X, which is 40 x plus two equals 66. It's a track to to both sides and four to the X equals 64 and then 64 is the same thing. This four to the third, so x is three. So in in quick of three yields and output of 66 meaning the 0.3 66 went beyond the graph

Were given some ordered pairs that are on the graph of F of X, and then we have a transformed function. Why? And we want to find the corresponding ordered pairs. So let's look at the transformations when you add extra to your shifting the whole Graf left to. So we can show that by subtracting two from each of the X coordinates. So the X coordinates would be negative to negative one and zero. And when you're subtracting one from the function, you're moving the whole thing down one and we can show that by subtracting one from each of the Y coordinates. So our new ordered pairs are negative to zero negative 11 and zero to.

So we want to suppose that 13 is a point on the graph of why equals G. Of X. So we want to know what is the point on the graph Y equals G. Of X plus three minus five. So we see that in this first part we're going to be um in part a we shift, yeah and we shift three units I left and five units down. So as a result of that we're going to have three units to the left that's gonna be negative 25 units down, that's going to be negative too. So it's going to be our next point. And then for the next one we're going to be shifting two units to the right. Um but then after we shifted to units to the right so that's three we're gonna multiply by -2. So in the X. Direction um or that in the X direction it's going to go to units to the right so it's gonna be three but in the y direction it's going to get multiplied. We're going to reflect it across the X. Axis that's going to go down negative. Um to start the negative six but increased by one. So it's a negative five. So we see that how these play a role these shifts and then also multiplying them by different factors, is going to shift the point itself.