Graphing Reciprocal Functions

How do you find the vertical asymptote of f(x) = 1/(x + 2)?

• Set the numerator equal to zero: 1 = 0

• Set the denominator equal to zero: x + 2 = 0, which gives the vertical asymptote at x = -2.

• Find the limit of f(x) as x approaches infinity

• Differentiate f(x) to find critical points.

What happens to the graph of f(x) = 1/x when x approaches 0?

• f(x) approaches a constant value.

• f(x) approaches infinity or negative infinity, indicating a vertical asymptote at x = 0.

• f(x) becomes undefined and has no limit.

• f(x) approaches zero.

What is a reciprocal function?

• A function that returns the square of the input.

• A function of the form f(x) = 1/x, where the output is the reciprocal of the input.

• A function that adds the input to itself.

• A function that multiplies the input by two.

How does the graph of f(x) = 1/x compare to f(x) = 1/(2x)?

• The graph of f(x) = 1/(2x) is vertically compressed compared to f(x) = 1/x.

• The graph of f(x) = 1/(2x) is vertically stretched compared to f(x) = 1/x.

• The graph of f(x) = 1/(2x) is identical to f(x) = 1/x.

• The graph of f(x) = 1/(2x) is shifted to the right compared to f(x) = 1/x.

What is the range of the function f(x) = 1/x?

• All real numbers

• All real numbers except for 0

• Only positive real numbers

• Only negative real numbers

What is a horizontal asymptote?

• A line that the graph of a function approaches as x approaches infinity or negative infinity.

• A vertical line that the graph of a function approaches as y approaches infinity.

• A point where the graph of a function intersects the x-axis.

• A curve that represents the maximum value of a function.

How does shifting a function to the left affect its graph?

• It moves every point on the graph 'h' units left, changing the function to f(x + h).

• It moves every point on the graph 'h' units right, changing the function to f(x - h).

• It reflects the graph across the y-axis, changing the function to f(-x).

• It stretches the graph vertically by a factor of 'h', changing the function to h*f(x).

What is the domain of the function f(x) = 1/(x + 1)?

• All real numbers

• All real numbers except x = -1

• All real numbers except x = 0

• All real numbers except x = 1

What is the effect of a negative sign in front of a reciprocal function?

• A negative sign reflects the graph across the x-axis.

• A negative sign shifts the graph to the right.

• A negative sign stretches the graph vertically.

• A negative sign changes the function to a quadratic.

What is the transformation of f(x) = 1/(x - 3) + 2?

• The function is shifted left by 3 units and down by 2 units compared to f(x) = 1/x.

• The function is shifted right by 3 units and down by 2 units compared to f(x) = 1/x.

• The function is shifted right by 3 units and up by 2 units compared to f(x) = 1/x.

• The function is reflected over the x-axis compared to f(x) = 1/x.