Question

graph the function below to find the y-intercept and state the domain, range, and the equation of the asymptote.\\( y = 3(11)^x \\)\
select all that apply.\
\\(\square\\) a) the y-intercept is 3.\
\\(\square\\) b) the y-intercept is 11.\
\\(\square\\) c) domain: all real numbers; range: \\( y > 0 \\)\
\\(\square\\) d) domain: all real numbers; range: \\( y < 0 \\)\
\\(\square\\) e) the asymptote is \\( y = 3 \\).\
\\(\square\\) f) the asymptote is \\( y = 0 \\).

Explanation:

Step1: Find y-intercept (set x=0)

Substitute $x=0$ into $y=3(11)^x$:
$y=3(11)^0 = 3(1) = 3$

Step2: Determine domain

For exponential functions $a(b)^x$, $x$ can be any real number, so domain is all real numbers.

Step3: Determine range

Since $11^x > 0$ for all real $x$, multiplying by 3 gives $3(11)^x > 0$, so range is $y>0$.

Step4: Find horizontal asymptote

As $x\to-\infty$, $11^x\to0$, so $y\to0$. Asymptote is $y=0$.

Answer:

A) The y-intercept is 3.
C) Domain: all real numbers; Range: $y > 0$
F) The asymptote is $y = 0$