Algebra C&C GMAS Practice Assessment

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What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It is characterized by its rapid growth or decay and has a constant percentage rate of change.

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What does the y-intercept of a function represent?

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The y-intercept of a function is the point where the graph of the function crosses the y-axis. It is the value of the function when x = 0.

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What does the x-intercept of a function represent?

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The x-intercept of a function is the point where the graph of the function crosses the x-axis. It is the value of x when the function equals zero (f(x) = 0).

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What does g(4) = 3.04 represent in a real-world context?

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g(4) = 3.04 indicates that the cost to make a container of grape jam in year 4 after the company opened was $3.04.

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How do you find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula f(n) = a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.

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What is the formula for the nth term of the arithmetic sequence where the first term is 5 and the fourth term is -4?

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The formula is f(n) = -3n + 8.

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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What does a decreasing linear function look like?

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A decreasing linear function has a negative slope, meaning as the value of x increases, the value of f(x) decreases.

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How can you determine if a set of data points can be modeled by a line of best fit?

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You can determine this by analyzing the trend of the data points. If the points show a consistent increase or decrease, they can likely be modeled by a linear function.

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What is the significance of the slope in a linear function?

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The slope of a linear function indicates the rate of change of the function. A positive slope means the function is increasing, while a negative slope means it is decreasing.