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College Algebra: Functions and Models - Section 1.1

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Termini in questo insieme (20)

  • What is a function?

    A function is a relation where each input has exactly one output.

  • Define domain in the context of a function.

    The domain is the set of all possible input values for a function.

  • Define range in the context of a function.

    The range is the set of all possible output values of a function.

  • In a function, what is the input and output?

    The input is the independent variable (usually x), and the output is the dependent variable (usually y).

  • How can you tell if a graph represents a function?

    A graph is a function if every vertical line intersects the graph at most once (Vertical Line Test).

  • What is the domain of \(y=\frac{3}{x}\)?

    The domain is all real numbers except 0 because division by zero is undefined.

  • What is the domain of \(y=\sqrt{x+5}\)?

    The domain is \(x \geq -5\) because the expression under the square root must be non-negative.

  • What is a scatter plot?

    A scatter plot is a graph that shows points representing pairs of data values.

  • What does function notation \(f(x)\) represent?

    \(f(x)\) denotes the output value of the function f at input x.

  • What is a mathematical model?

    A mathematical model is a mathematical representation of a real-world situation using functions or equations.

  • In the context of functions, what is the independent variable?

    The independent variable is the input variable that you choose freely, often denoted as x.

  • In the context of functions, what is the dependent variable?

    The dependent variable depends on the independent variable and is often denoted as y.

  • How do you determine if a table defines a function?

    If each input value corresponds to exactly one output value, the table defines a function.

  • Is weight a function of the day if weight values repeat on different days?

    Yes, because each day (input) has exactly one weight (output), even if weights repeat on different days.

  • What is the domain of \(y=20-x\)?

    The domain is all real numbers, \((-\infty, \infty)\).

  • Does the temperature on a given day define a function?

    Yes, because each day has exactly one temperature value.

  • Interpret \(f(10)=26\) if f represents average car cost in thousands since 2000.

    In the 10th year since 2000 (i.e., 2010), the average cost of a new car was \$26,000.

  • What does it mean if a relation is not a function?

    It means at least one input corresponds to more than one output.

  • How to treat variables when asked if x is a function of P?

    Treat P as the input (independent variable) and x as the output (dependent variable).

  • What value of t represents the year 2025 if t is years after 2000?

    \(t=25\) because 2025 is 25 years after 2000.