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Unit 1 Algebra 2 Semester 2
Terms in this set (16)
A proportion is an equation that states that two ratios are equal. A proportion of the form = is true if the cross products are equal, so that ad = bc.
A rational expression has the form , where A and B are polynomials.
When is a rational expression equal to zero?
A rational expression equals zero when the numerator equals zero.
When is a rational expression undefined?
A rational expression is undefined when the denominator equals zero.
How do you simplify a rational expression?
1. Factor the numerator and denominator.2. Find the GCF of the numerator and denominator.3. Divide out the GCF from the numerator and denominator.4. Decide what value(s) the variable cannot equal.
How do you multiply two rational expressions?
If and A/B and C/D are rational expressions, then A/B x C/D = AC/BD
How do you divide two rational expressions?
If A/B and C/D are rational expressions, then A/B divided by C/D =A/B x C/D= AD/BC
How do you use the LCM to find a common denominator?
1. Factor the denominator of each rational expression.
2. Find the least common multiple (LCM) of the denominators.
3. Multiply the numerator and denominator of each rational expression by the factor(s) that make the denominator the LCM.
What is direct variation?
In a relationship of direct variation, one variable is a constant multiple of another. If you increase the input, the output increases proportionally. (STRAIGHT LINE)
What is inverse variation?
In a relationship of inverse variation, the quantities change inversely. So, as one quantity gets bigger, the other one gets smaller. If you increase the input, the output decreases proportionally. (CURVED LINE)
What is a rational function?
A rational function is a function whose equation contains a rational expression.
What is an asymptote?
An asymptote of a function is a line that the graph of the function gets closer and closer to but never touches.
What is a vertical asymptote?
A vertical asymptote is a line that represents an x-value where a function is undefined. The function's values become very large positive or small negative numbers as they approach a vertical asymptote.
What are the steps for graphing a rational function?
1. Determine where the vertical asymptote(s) are located — that is, where the function is undefined and approaches + or as it nears the point of discontinuity.
2. Make a table of values to find points on the graph near the asymptotes.
How do you sketch a rational function whose numerator is a number and whose denominator is a factored polynomial?
1. A function that has a constant not equal to zero for its numerator and a factored polynomial for its denominator will have a vertical asymptote at every x-value for which its denominator is zero.
2. Make a table for each vertical asymptote to find out what happens to the function near the asymptote.
3. Draw the function based on the table.
What is the process for sketching rational functions?
Create a sign chart by following these steps:
1. Find all of the function's zeros and vertical asymptotes, plot them on a number line, and label them as zeros or asymptotes.
2. Pick test numbers before and after each of the function's zeros and asymptotes. Check whether the function is positive or negative at these numbers by substituting them into the function's equation.
3. Use the results of Step 2 to fill in the signs on your sign chart.
Sketch the function's graph, plotting additional points as guides when needed.
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