Question

question 2 (essay worth 2 points) (05.06r hc) using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? explain your reasoning.

Explanation:

Step1: Define x-intercept condition

The x-intercept occurs where $g(x) = 0$, so set up the equation:
$$\log(x + 4) = 0$$

Step2: Convert log to exponential form

Recall $\log(a)=b$ means $10^b=a$ (common log base 10):
$$x + 4 = 10^0$$

Step3: Simplify and solve for x

Calculate $10^0=1$, then isolate x:
$$x + 4 = 1 \implies x = 1 - 4 = -3$$

Step4: Verify domain validity

Check that $x+4>0$: $-3 + 4 = 1 > 0$, which is valid.

Answer:

The x-intercept is $x=-3$, or the point $(-3, 0)$. This is found by setting $g(x)=0$, converting the logarithmic equation to its exponential form, solving for $x$, and confirming the value satisfies the domain requirement of the logarithm (argument must be positive).