Exploring Rational Expressions in Honors Algebra 2

The video tutorial covers key features of functions, including domain, range, and intercepts. It analyzes quadratic, absolute value, and piecewise functions, discussing their properties and graph behavior. A word problem involving a car's gasoline usage is solved using linear equations. The tutorial concludes with an analysis of graph behavior, focusing on positive, negative, increasing, and decreasing intervals.

What is the definition of a function?

• Every input has one output.

• Every output has one input.

• There are multiple outputs for each input.

• There are multiple inputs for each output.

What is the domain of a quadratic function that extends infinitely in both directions?

• Numbers between -10 and 10

• All real numbers

• Only positive numbers

• Only negative numbers

What is the range of a quadratic function with a maximum value of 0?

• y ≤ 0

• 0 < y < 10

• y ≥ 0

• All real numbers

What is the x-intercept of the quadratic function discussed?

• (3, -9)

• (0, -9)

• (0, 3)

• (3, 0)

What is the domain of an absolute value function that extends infinitely in both directions?

• All real numbers

• Only positive numbers

• Only negative numbers

• Numbers between -5 and 5

What is the range of an absolute value function with a minimum value of 0?

• All real numbers

• y ≥ 0

• 0 < y < 10

• y ≤ 0

What is the x-intercept of the absolute value function discussed?

• (0, 2)

• (0, 0)

• (0, -2)

• (2, 0)

What is the domain of a piecewise function with gaps in the middle?

• All real numbers except for the gaps

• Only positive numbers

• Only negative numbers

• Numbers between -10 and 10

What does the x-intercept of 320 in the word problem represent?

• The car has traveled 320 miles and has 16 gallons of gas left.

• The car has 320 gallons of gas left.

• The car has traveled 320 miles and has 0.05 gallons of gas left.

• The car has traveled 320 miles and has no gas left.

What does the y-intercept of 16 in the word problem represent?

• The car has traveled 16 miles.

• The car has 16 miles left to travel.

• The car has 0.05 gallons of gas left.

• The car starts with 16 gallons of gas.