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laiz [17]
3 years ago
13

Using a chart of values, graph the function f(x)=3^x

Mathematics
2 answers:
Citrus2011 [14]3 years ago
8 0
Hey there!

For this problem, I would assume that you must make your own chart of values. You can do this by simply plugging in numbers like 1, 2, 3, etc... Since your graph won't be linear, you might want to do some negative numbers, as well. 

Also because your graph isn't linear, you might want to figure out or determine on your own just how far your curve will go. You can then figure out how many times you need to plug in an additional numbers for your function to then graph. 

I've attached a digital graph of this function, perhaps you can find it useful. 

Hope this helped you out! :-)

Ivan3 years ago
4 0
Let's approach this by understanding how an exponential works, to begin.

Any exponential in the form: f(x) = 3^{x} will cut the y-axis once and once only. This is because the exponential graph is a monotonic increasing graph for all real values of x.

We can prove this by taking the derivative. When we take the derivative of a function, we are finding the slope or gradient of the function at an arbitrary point on the graph.

\text{Differentiating the function:} f'(x) = \frac{d(3^{x})}{dx}
f(x) = e^{ln(3^{x})}
f(x) = e^{xln3}
f'(x) = ln(3) \cdot e^{xln3}

Thus, we can conclude for any value of x, the gradient will always be increasing. Now, by plotting some critical values, we can find that the graph hits the y-axis once and once only at the value y = 1.

At this point, we've sort of have an idea as to what the graph will do, but the most critical points are the endpoints, when x approaches infinity and negative infinity. In order to understand what they do at those points, instead of plotting those points, let's use a limit.

\lim_{x \to \pm \infty}(3^{x})

Limits are a crucial tool in understanding what a graph does as the terms get arbitrarily huge and infinitesimally small. We can see that as x approaches infinity, we approach some really big number faster than a  quadratic, linear line, and any function other than factorials.

However, let's approach the negative side. If we were to plug in negative infinity into the function, we get:
f(-\infty) = 3^{-\infty}
f(-\infty) = \frac{1}{3^{\infty}}

Now, we know that for a really big number in the denominator, the function will shrink smaller and smaller to a value, 0. Because the numerator is positive, we can see that the graph will NEVER hit below 0. So, we can conclude that the graph has a limit at x ≠ 0.

Since we know the endpoints, the gradient at any value, and the y-intercept, we can graph the function. Refer to the other answer for the correct graph of 3ˣ.
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3 years ago
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pantera1 [17]

Answer:

-11/20

Step-by-step explanation:

    2      8   1

 (0-— ÷ (0-—))+—

    3      9   5

           8

Simplify   —

           8/9

2         8     1

 (0 -  — ÷ (0 -  —)) + —

       3         9     5

Simplify   —

           2/3

2   -8     1

 (0 -  — ÷ ——) +  —

       3   9      5

2      -8

Divide  —  by  ——

        3      9

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

2     -8       2      9

—  ÷  ——   =   —  •  ——

3     9        3     -8

(0--3/4)+1/5

Least Common Multiple:

     20

Left_M = L.C.M / L_Deno = 5

Right_M = L.C.M / R_Deno = 4

      3 • 5 + 4                 -11

—————————  =  ———

      20                            20

-11/20

3 0
3 years ago
Read 2 more answers
Solve the system
Helga [31]
The answer is actually choice A

---------------------------------------------------------
---------------------------------------------------------

If we add up the equations straight down we will have 0a+2b = 6

Note how adding the 'a' terms gives us 3a + (-3a) = 3a-3a = 0a. The 0a term is really 0 since 0 times anything is 0. So the 'a' terms will go away

The equation 0a+2b = 6 turns into 0+2b = 6 and that simplifies to 2b = 6

To isolate b, we divide both sides by 2

2b = 6
2b/2 = 6/2
b = 3

We can stop here since only one answer choice has b = 3, which is choice A. However, let's keep going to find the value of 'a'

Plug b = 3 into any equation with 'a' and 'b', then solve for 'a'

3a+4b = 9
3a+4*3 = 9
3a+12 = 9
3a+12-12 = 9-12
3a = -3
3a/3 = -3/3
a = -1

So a = -1 and b = 3 pair up to form (a,b) = (-1,3)

--------------------------------------

To check, plug this ordered pair back into both equations

Equation 1:
3a+4b = 9
3*(-1)+4*3 = 9
-3+12 = 9
9 = 9
Equation 1 has been checked out

Equation 2:
-3a-2b = -3
-3(-1)-2(3) = -3
3 - 6 = -3
-3 = -3
this is true as well

So this confirms that the final answer is choice A
8 0
2 years ago
Read 2 more answers
Money is collected from citizens and businesses by the government in the form of what
padilas [110]
The answer is 3)Taxes
6 0
2 years ago
Read 2 more answers
A square pyramid is shown:
Colt1911 [192]
Area of triangles:
0.5x9=4.5
4.5x2=9 (i divided 4 (the amount of triangles) by 2 instead of dividing 4.5 by 2)

area of square:
0.5x0.5=0.25

surface area of whole thing:
9+0.25=9.25

so the answer is 9.25

hope this helps :)
7 0
2 years ago
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