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Graphs of Functions: Intercepts and Domain

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  • What is the x-intercept of a graph?
    The x-intercept is the point(s) where the graph crosses the x-axis, meaning y = 0.
  • How do you find the x-intercept from a graph?
    Identify the point(s) where the graph crosses the x-axis; these points have coordinates where y = 0.
  • What is the domain of a function?
    The domain is the set of all possible x-values for which the function is defined.
  • How is the domain written in set-builder notation?
    The domain is written as {x | condition on x}, where the condition describes all valid x-values.
  • How do you determine the domain from a graph?
    Look at the leftmost and rightmost points on the graph along the x-axis, noting if endpoints are included or excluded.
  • Give an example of domain in set-builder notation for a function defined from x = -2 to x = 5 including endpoints.
    The domain is {x | -2 \(\leq\) x \(\leq\) 5}.
  • What does an open circle on a graph endpoint indicate about the domain?
    An open circle means the endpoint is excluded from the domain, so use parentheses in interval notation.
  • What does a closed circle or solid line endpoint indicate about the domain?
    A closed circle or solid line means the endpoint is included in the domain, so use brackets in interval notation.
  • What does it mean to find x when f(x) = 5 from a graph?
    It means finding the x-value(s) where the graph's y-coordinate is 5.
  • How do you find the x-value where f(x) = 5 on a graph?
    Draw a horizontal line at y = 5 and find the x-coordinate(s) where this line intersects the graph.
  • Give an example of finding x when f(x) = 5.
    If the graph crosses y = 5 at x = 3, then f(3) = 5.
  • What does f(a) represent in a function?
    f(a) is the value of the function at the input x = a.
  • How do you find f(1) from a graph?
    Locate x = 1 on the x-axis, move vertically to the graph, then read the corresponding y-value.
  • Give an example of evaluating a function at x = 1 using a graph.
    If the graph passes through (1, 4), then f(1) = 4.
  • What is the range of a function?
    The range is the set of all possible y-values that the function attains.
  • How do you determine the domain from a graph?
    Look at the leftmost and rightmost points of the graph along the x-axis to find the interval of x-values.
  • How do you determine the range from a graph?
    Look at the lowest and highest points of the graph along the y-axis to find the interval of y-values.
  • How do you decide whether to use brackets or parentheses in interval notation for domain or range?
    Use brackets [ ] if endpoints are included (closed circle), and parentheses ( ) if excluded (open circle).
  • Give an example of domain and range in interval notation.
    Domain: [-3, 5], Range: (0, 7] means x is from -3 to 5 inclusive, y is greater than 0 up to 7 inclusive.
  • What is the Cartesian coordinate system?
    A plane defined by a horizontal x-axis and a vertical y-axis used to locate points.
  • How do you plot the point (-2, 3) on the Cartesian plane?
    Start at the origin, move 2 units left (negative x), then 3 units up (positive y), and mark the point.
  • What is the x-intercept of a graph?
    The point(s) where the graph crosses the x-axis, where y = 0.
  • What is the y-intercept of a graph?
    The point where the graph crosses the y-axis, where x = 0.
  • How do you find the x-intercepts from a graph?
    Look for points where the graph crosses the x-axis; these points have y = 0.
  • How do you find the y-intercept from a graph?
    Find the point where the graph crosses the y-axis; this point has x = 0.
  • Give an example of x and y intercepts.
    If a graph crosses the x-axis at (4, 0) and the y-axis at (0, -1), then x-intercept is 4 and y-intercept is -1.