A. plot the data for the functions f(x) and g(x) on a grid and connect the points. x -2 -1 0 1 2 f(x) 1/9 1/3 1 3 9 x -2 -1 0 1 2 g(x) -4 -2 0 2 4 b. which function could be described as exponential and which as linear? explain. c. if the functions continue with the same pattern, will the function values ever be equal? if so, give estimates for the value of x that will make the function values equals. if not, explain why the function values will never be equal.
a) see the attached graph
b) f(x) is exponential. It matches the equation f(x) = 3^x.
g(x) is linear. It matches the equation g(x) = 2x.
c) The line misses the curve so does not intersect anywhere. There is no value of x for which the functions are equal.
a) see the plots below
b) f(x) is exponential; g(x) is linear (see below for explanation)
c) the function values are never equal
a) a graph of the two function values is attached
b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).
c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.
In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.
1. The graph with the appropriate plots is in the PDF. I'm sorry for that inconvenience.
2. The function f(x) is an exponential function and g(x) is a linear. F(x) is exponential because it slowly starts to increase and then once it passes (0, 1), it increases significantly, this represents a exponential growth. G(x) is linear because the line it has on the graph is consistent and represents a straight line. Hence, why they call it a linear function.
3. The function values moving left to right, gradually increase.
4. The best I can come up with for the function values being equal is (1.09, 5.1) The points aren't exactly on a whole number so it's hard to estimate or give an exact number.
I hope this helps you, mark as brainliest, please. I spent quite a bit of time on this.
The first thing you have to do is study the graph. The two functions are
f(x) = 4^x That's the curved graph. (in red)
g(x) = x + 4. That's the straight line. (in blue)
You know that the first one is not a linear relationship because the x values go from integer values -2 to 2 (including 0). The y values are a bit different. They go from 1/16 to 16 with those integer values. So you could try y = 4^(-x). It doesn't work, but you could try it. It gives the table numbers for y in the reverse order that the table you are given goes. For x you get -2 -1 0 1 2 and for y you would get 16 4 1 1/4 1/16.
You could try y = (1/4)^x
For this try, you would get x = -2 -1 0 1 2 and for y = 16 4 0 1/4 and 1/16
but that doesn't work either.
You could try until you get y = 4^x which does work.
g(x) is a lot easier to deal with. It looks better behaved. as x goes up, so does y. You will find that the y values obey y = x + 4. You could try other lines, but that one works. Many times it's just a guess