Finals Review Sem 1 Linear/Exponential/ comb like terms

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base (a positive real number), and x is the exponent. The graph of an exponential function increases or decreases rapidly.

Front

What are like terms in algebra?

Back

Like terms are terms that have the same variable raised to the same power. For example, 5x and -8x are like terms because they both contain the variable x.

Front

How do you simplify the expression 3(2a + 5) + 5(a - 2)?

Back

First, distribute: 3(2a) + 3(5) + 5(a) - 5(2) = 6a + 15 + 5a - 10. Then combine like terms: 6a + 5a + 15 - 10 = 11a + 5.

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise over run).

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What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How can you identify a linear relationship from a table of values?

Back

A linear relationship will show a constant rate of change between the x and y values. If the difference in y values divided by the difference in x values is constant, the relationship is linear.

Front

What is the difference between a coefficient and a constant?

Back

A coefficient is a numerical factor in front of a variable (e.g., in 5x, 5 is the coefficient). A constant is a fixed value that does not change (e.g., in the expression 3x + 4, 4 is the constant).

Front

What is the formula for finding the nth term of a linear sequence?

Back

The nth term of a linear sequence can be found using the formula: T(n) = a + (n-1)d, where a is the first term and d is the common difference.

Front

What is the formula for finding the nth term of an exponential sequence?

Back

The nth term of an exponential sequence can be found using the formula: T(n) = a * r^(n-1), where a is the first term and r is the common ratio.