Evaluate the exponential equation for three values of x greater than -4, three values of x smaller than -4, and at x = -4. Show your work. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic to the graph y=3^x+4+1
y = 3^x = 4 + 1 = 3^x + 5.
y = 3^-5 + 5 = 0.00412 + 5 = 5.00412,
y = 3^-4 + 5 = 0.012 + 5 = 5.012
y = 3^-2 = 0.1111 + 5 = 5.1111
(-5 , 5.0041) , (-4 , 5.012) , (-2 , 5.1111).
4.012-S=3.313
To evaluate the exponential equation y = 3^x + 4 + 1 for different values of x, we can substitute the values of x into the equation and calculate the corresponding values of y. Let's start by evaluating the equation for three values of x greater than -4:
1. For x = -3:
y = 3^(-3) + 4 + 1
y = 1/27 + 4 + 1
y ≈ 4.037
2. For x = -2:
y = 3^(-2) + 4 + 1
y = 1/9 + 4 + 1
y ≈ 5.111
3. For x = -1:
y = 3^(-1) + 4 + 1
y = 1/3 + 4 + 1
y ≈ 5.333
Now, let's evaluate the equation for three values of x smaller than -4:
1. For x = -5:
y = 3^(-5) + 4 + 1
y = 1/243 + 4 + 1
y ≈ 5.004
2. For x = -6:
y = 3^(-6) + 4 + 1
y = 1/729 + 4 + 1
y ≈ 5.001
3. For x = -7:
y = 3^(-7) + 4 + 1
y = 1/2187 + 4 + 1
y ≈ 5.0005
Finally, let's evaluate the equation for x = -4:
For x = -4:
y = 3^(-4) + 4 + 1
y = 1/81 + 4 + 1
y ≈ 5.012
Now we have the following ordered pairs:
(-3, 4.037)
(-2, 5.111)
(-1, 5.333)
(-5, 5.004)
(-6, 5.001)
(-7, 5.0005)
(-4, 5.012)
By plotting these points on a graph, we can observe the shape of the exponential function. Additionally, since the value of y approaches infinity as x approaches negative infinity, there is no line asymptotic to the graph given by y = 3^x + 4 + 1.