I really need help on these problems. I am lost. Don't have an idea of where to begin in solving and graphing these. Please see attachment. Thanks to anyone who can help. It is greatly appreciated.
If you plotted the points, it is quite evident that it's an exponential function. You can see that it quickly "explodes" rapidly heading off to infinity.
Domain: (-inf, inf)
Range: (0, inf)
a.) x - 2*sqrt(x) = 0
-2*sqrt(x) = x
sqrt(x) = x/(-2)
Square both sides
x = x^2/4
4x = x^2
0 = x^2 - 4x
0 = x*(x - 4)
x = 0 V x = 4
b.) You should be able to graph y = x; it has a slope of 1 and y-intercept of 0. For y = 2*sqrt(x), plug in values and it will be evident what it looks like.
Note any negative values are undefined.
So, for instance, plot:
(0, 0)
(1, 2)
(4, 4)
(9, 6)
(16, 8)
.
.
.
The point of intersection is when the two graphs are equal.
This occurs at x = 0 ^ x = 4, and is very obvious by looking at a graph. Or, using algebra,
2*sqrt(x) = x
Which we solved earlier.
Go graph it on paper.
The graph looks like a Nike Swoosh that exercised too much it looks as thin as a curved line.
The graph is exponential.
Because of that thinniest Nike Swoosh appearance, and because
0.333 = (0.111)*3
1 = (0.333)*3 = [(0.111)*3]*3 = (0.111)*3^2
3 = 1*3 = [(0.111)*3^2]*3 = (0.111)*3^3
.
.
an = (a1)*3^n
Domain is all values of x, from after negative infinity up to before positive infinity.
Range is all positive values of y, from just above zero up to before positive infinity.
Hello, fw_mathis!
$\displaystyle \begin{array}{ccccccc}x &| & -2 & -1 & 0 & 1 & 2\\
\hline y & | & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9
\end{array}$
(a) Given the table above, graph the function.
(b) Identify the graph of the function (line, parabola, hyperbola, or exponential).
(c) Explain your choice and give the domain and range as shown on the graph.
(d) Give the domain and range of the entire function.
(a) I assume you know how to plot points . . .
(b) We have an exponential function: .$\displaystyle y \:=\:3^x$
(c) The domain is: .$\displaystyle [-2,\,2].$. .The range is: .$\displaystyle \left[\frac{1}{9},\,9\right]$
(d) For the entire function, the domain is: .$\displaystyle (-\infty,\infty)$. . .The range is: .$\displaystyle (0,\,\infty) $.