Answer:
1) Domain: -∞ < x < +∞
2) Range: y > 0
3) y intercept: (0, 200)
4) Asymptote: y = 0
5) The growth rate; r = 0.08
6) The growth factor = 1.08
7) End Behavior: As x → -∞, f(x) → 0
8) End Behavior: As x → +∞, f(x) → +∞
Step-by-step explanation:
1) The domain of the function is given as the x values for which the function is valid which includes from -∞ < x to +∞
2) The range of the function, are the range of the output values of the function for the given range of the input values
For the function, f(x) = 200·(1.08)ˣ, we have, f(x) = y > 0, for all values of x
3) The y-intercept is the value of y, when x = 0, given as follows;
y intercept = f(0) = 200·(1.08)⁰ = 200 × 1 = 200
4) The asymptote is the line that the function approaches but never reaches
In the question, as x tends to -∞, the function f(x) approaches 0. Therefore, f(x) = y = 0 is the asymptote of the function
5) The growth rate of an exponential function, y = a(1 + r)ˣ is r
Therefore, for the function, 200·(1.08)ˣ, which is equivalent to 200·(1 + 0.08) ˣ, the growth rate = 0.08
6) The growth factor of an exponential function, y = a(1 + r)ˣ is (1 + r)
Therefore, for the function, 200·(1.08)ˣ, which is equivalent to 200·(1 + 0.08) ˣ, the growth factor = (1 + 0.08) = 1.08
7) The end behavior as x tends to -∞, [tex]f(x) = y= 200 \cdot (1.08) ^{-\infty} \rightarrow 0[/tex]
8) The end behavior as x tends to +∞, [tex]f(x) = y= 200 \cdot (1.08) ^{-#+\infty} \rightarrow + \infty[/tex]
