Question

sketch the graph of the following function, and state its domain and range.

f(x) = -1 + log (x + 6)

list ordered pairs that satisfy the equation.

x	-5	-3	4

(round to the nearest tenth as needed.)

Explanation:

Step1: For \( x = -5 \)

Substitute \( x = -5 \) into \( f(x)=-1+\log(x + 6) \). First, calculate \( x + 6=-5 + 6 = 1 \). Then \( \log(1)=0 \) (assuming base 10, if it's natural log, \( \ln(1)=0 \) too). So \( f(-5)=-1 + 0=-1 \).

Step2: For \( x = -3 \)

Substitute \( x=-3 \) into the function. \( x + 6=-3 + 6 = 3 \). Then \( \log(3)\approx0.477 \). So \( f(-3)=-1+\log(3)\approx-1 + 0.5=-0.5 \) (rounded to nearest tenth).

Step3: For \( x = 4 \)

Substitute \( x = 4 \) into the function. \( x + 6=4 + 6 = 10 \). Then \( \log(10)=1 \) (base 10). So \( f(4)=-1 + 1=0 \).

Answer:

For \( x=-5 \), \( f(x)=-1 \); for \( x = -3 \), \( f(x)\approx-0.5 \); for \( x = 4 \), \( f(x)=0 \)

So the ordered pairs are \((-5, -1)\), \((-3, -0.5)\), \((4, 0)\) and the table values are \(-1\), \(-0.5\), \(0\) respectively.