Question

1. y = log x

Answer 1

Answer:

Domain {x : x  > 1}

Range {y : y ∈ R}

Vertical asymptote x = 0

x-intercept (1, 0)

End behavior consistent

Graph attached down

Step-by-step explanation:

Let us study the equation:

∵ y = log(x)

→ It is a logarithmic function, so no negative values for x

∴ Its domain is {x : x  > 1}

∴ Its range is {y : y ∈ R}, where R is the set of the real numbers

→ An asymptote is a line that a curve approaches, but never touches

∵ x can not be zero

∴ It has a vertical asymptote whose equation is x = 0

→ x-intercept means values of x at y = 0, y-intercept means

   values of y at x = 0

∵ x can not be zero

∴ There is no y-intercept

∵ y can be zero

∴ The x-intercept is (1, 0)

→ The end behavior of the parent function is consistent.

   As x approaches infinity, the y-values slowly get larger,

   approaching infinity

∵ y = log(x) is a parent function

∴ The end behavior is consistent

→ The graph is attached down