Finding the domain and X-intercepts of a logarithm with horizontal shift

The video tutorial covers graph shifting, algebraic representation of shifts, domain and vertical asymptote explanation, handling negative values in functions, graph reflection, and finding intercepts. The instructor uses examples to demonstrate how to shift graphs algebraically and determine domains and asymptotes. The tutorial also explains how to handle negative values and calculate intercepts using logarithmic and exponential forms.

What happens to the graph when you have an X + 2 inside the function?

• It compresses the graph horizontally.

• It shifts the graph to the right.

• It stretches the graph vertically.

• It shifts the graph to the left.

How do you determine the domain of a function with an expression inside?

• Set the expression greater than zero.

• Set the expression less than zero.

• Set the expression equal to one.

• Set the expression equal to zero.

What is the vertical asymptote of a function with X + 2 inside?

• X = 1

• X = -2

• X = 0

• X = 2

If the expression inside the function is negative, what must you do to the inequality?

• Multiply by zero.

• Subtract 1 from both sides.

• Flip the inequality sign.

• Add 1 to both sides.

How do you find the X-intercept of a logarithmic function?

• Set y equal to 1.

• Set y equal to zero and convert to exponential form.

• Set the base of the log to zero.

• Set the inside of the log to one.

What is the result of converting log base three of X + 2 to exponential form when y = 0?

• 3^-1 = X + 2

• 3^1 = X + 2

• 3^0 = X + 2

• 3^2 = X + 2

What is the X-intercept of the function after solving 3^0 = X + 2?

• X = -1

• X = 1

• X = 2

• X = 0