Exploring Rational Functions: Adding and Subtracting Expressions

What happens to the graph of y=1/x as x approaches zero?

• The graph expands infinitely in the y-direction.

• The graph has an undefined point at x=0.

• The graph becomes a straight line.

• The graph touches the x-axis.

Why does the graph of a rational function never touch the x-axis at x=0?

• Because the function is undefined at x=0.

• Because the function equals zero at x=0.

• Because the function has a maximum value at x=0.

• Because the function has a minimum value at x=0.

What does the graph of y=1/x look like?

• A parabola opening upwards.

• A curve approaching the x-axis and y-axis but never touching them.

• A circle centered at the origin.

• A straight line passing through the origin.

What is a key characteristic of the graph of a rational function?

• It always crosses the x-axis.

• It has a constant slope.

• It has an undefined point at x=0.

• It is symmetrical about the y-axis.

What defines a rational function?

• A function that cannot be graphed.

• A function that only contains whole numbers.

• A function that is a fraction with a variable in the denominator.

• A function that can be expressed as a fraction with a variable in the numerator.

What is the parent function of a rational function?

• y = 1/x

• y = x/2

• y = x^2

• y = x

How do you find the x-intercept of a rational function?

• By setting the numerator equal to zero.

• By setting y equal to zero.

• By setting the denominator to zero.

• By setting x equal to zero.

What is the y-intercept of a rational function found by?

• Multiplying the numerator by zero.

• Setting x equal to zero and solving for y.

• Dividing the denominator by zero.

• Setting y equal to zero and solving for x.

How can the x-intercepts of a rational function in factored form be found?

• By setting the denominator to zero.

• By finding the roots of the numerator.

• By dividing the numerator by the denominator.

• By multiplying the factors of the numerator.

What role does the numerator play in determining the x-intercepts of a rational function?

• The numerator does not affect the x-intercepts.

• The numerator must be equal to the denominator.

• The numerator must be zero.

• The numerator must be a prime number.