Transformation and Add/Subtract Rational Expressions

Front

What is a transformation in the context of functions?

Back

A transformation refers to a change in the position, size, or shape of a function's graph, which can include shifts, reflections, stretches, and compressions.

Front

What does it mean to shift a function left or right?

Back

Shifting a function left or right involves moving the graph horizontally along the x-axis. A positive shift moves it to the right, while a negative shift moves it to the left.

Front

What does it mean to shift a function up or down?

Back

Shifting a function up or down involves moving the graph vertically along the y-axis. A positive shift moves it up, while a negative shift moves it down.

Front

What is the parent function of g(x)=1/x?

Back

The parent function g(x)=1/x is a rational function that represents a hyperbola with asymptotes at the x-axis and y-axis.

Front

How do you find the least common denominator (LCD) of rational expressions?

Back

To find the LCD, identify the least common multiple of the denominators, considering all factors and their highest powers.

Front

What is the process of adding rational expressions?

Back

To add rational expressions, first find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What are excluded values in rational expressions?

Back

Excluded values are values of the variable that make the denominator zero, which are not allowed in the domain of the function.

Front

What is the effect of reflecting a function over the x-axis?

Back

Reflecting a function over the x-axis changes the sign of the output values (y-values), resulting in a mirror image of the graph across the x-axis.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression involves reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Front

What is the significance of the transformation 'shift left 3 units'?

Back

This transformation means that every point on the graph of the function is moved 3 units to the left on the x-axis.