Question

1. the parent function $y = \log(x)$ has which of the following attributes:

an x intercept at (1, 0)
d: $(0, \infty)$
d: $x \in \mathbb{r}$
r: $y \in \mathbb{r}$
an y intercept at (0, 1)
vertical asymptote at x=0

Explanation:

Step1: Check x-intercept

To find x-intercept, set $y=0$:
$0 = \log(x) \implies x=10^0=1$. So x-intercept is $(1,0)$.

Step2: Check domain

Logarithm function $\log(x)$ is defined only for $x>0$, so domain $D: (0, \infty)$.

Step3: Check range

Logarithm function outputs all real numbers, so range $R: y \in \mathbb{R}$.

Step4: Check y-intercept

To find y-intercept, set $x=0$: $\log(0)$ is undefined, so no y-intercept at $(0,1)$.

Step5: Check vertical asymptote

As $x \to 0^+$, $\log(x) \to -\infty$, so vertical asymptote at $x=0$.

Answer:

An x intercept at (1, 0)
D: $(0, \infty)$
R: $y \in \mathbb{R}$
vertical asymptote at x=0