IM Algebra Unit 4 Test

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What is a function?

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A function is a relation that assigns exactly one output for each input. It can be represented by an equation, a graph, or a table.

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What does the inverse function represent?

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The inverse function gives the input value when the output value is known. For example, if a function gives the cost based on visits, the inverse gives the number of visits based on the cost.

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How do you write a function in function notation?

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Function notation is written as f(x) = expression, where f is the function name, x is the input variable, and the expression defines the output.

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What is a piecewise function?

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A piecewise function is a function that has different rules or expressions for different intervals of the input.

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How do you evaluate a function at a specific input?

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To evaluate a function at a specific input, substitute the input value into the function's equation and simplify.

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What is the cost function for a gym visit defined as c(n) = 50 + 4n?

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This function represents the total monthly cost in dollars for visiting the gym n times, where 50 is the base fee and 4 is the cost per visit.

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If c(8) = 82, what does this mean in context?

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It means that if a person visits the gym 8 times in a month, the total cost will be $82.

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

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The slope indicates the rate of change of the function. In the context of cost functions, it represents the cost per additional unit (e.g., per gym visit).

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How do you find the remaining amount in a function like g(w) = 10000 - 850w?

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To find the remaining amount after w weeks, substitute the number of weeks into the function and calculate the result.

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What does it mean if a function is not connected?

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If a function is not connected, it means there are gaps in the output values for certain input values, indicating that not all inputs produce valid outputs.