Question

Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning

FLVS Algebra II

Answer 1

x = - 3

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The x-intercept of a function represents the point at which the graph of the function crosses the x-axis.

To find the x-intercept of g(x) = log(x + 4), we consider that the x-intercept of the parent function f(x) = log(x) is x = 1:

• log(x) = 0 ⇒ x = 10⁰ = 1

Since g(x) is the translation of f(x) 4 units left, we can set up equation:

• x + 4 = 1
• x = 1 - 4
• x = -3

Therefore, the x-intercept of g(x) = log(x + 4) is x = - 3.