Skip to main content
Indietro

Precalculus: Chapter 2 - Graphs

I pulsanti di controllo sono stati cambiati in modalità "navigazione".
1/20

Termini in questo insieme (20)

  • What is the definition of a function in terms of graphs?
    A function is a relation where each input (x-value) has exactly one output (y-value) on the graph.
  • What does the vertical line test determine?
    The vertical line test determines if a graph represents a function by checking if any vertical line intersects the graph more than once.
  • How do you find the x-intercept of a graph?
    The x-intercept is found where the graph crosses the x-axis, so set y = 0 and solve for x.
  • How do you find the y-intercept of a graph?
    The y-intercept is where the graph crosses the y-axis, so set x = 0 and solve for y.
  • What is the domain of a function?
    The domain is the set of all possible input values (x-values) for which the function is defined.
  • What is the range of a function?
    The range is the set of all possible output values (y-values) that the function can produce.
  • How is a function's graph affected by a vertical shift?
    A vertical shift moves the graph up or down by adding or subtracting a constant to the function's output.
  • How is a function's graph affected by a horizontal shift?
    A horizontal shift moves the graph left or right by adding or subtracting a constant inside the function's input.
  • What does it mean for a function to be increasing on an interval?
    A function is increasing on an interval if the y-values rise as the x-values move from left to right.
  • What does it mean for a function to be decreasing on an interval?
    A function is decreasing on an interval if the y-values fall as the x-values move from left to right.
  • What is an even function and how is it identified on a graph?
    An even function satisfies f(-x) = f(x) and its graph is symmetric about the y-axis.
  • What is an odd function and how is it identified on a graph?
    An odd function satisfies f(-x) = -f(x) and its graph is symmetric about the origin.
  • How do you reflect a graph across the x-axis?
    Multiply the function by -1, changing f(x) to -f(x), which flips the graph over the x-axis.
  • How do you reflect a graph across the y-axis?
    Replace x with -x in the function, changing f(x) to f(-x), which flips the graph over the y-axis.
  • What is the effect of vertical stretching on a graph?
    Multiplying the function by a factor greater than 1 stretches the graph away from the x-axis vertically.
  • What is the effect of vertical compression on a graph?
    Multiplying the function by a factor between 0 and 1 compresses the graph toward the x-axis vertically.
  • How do you determine if a function is one-to-one from its graph?
    A function is one-to-one if every horizontal line intersects the graph at most once (horizontal line test).
  • What is the significance of the slope in a linear graph?
    The slope represents the rate of change or steepness of the line, calculated as rise over run.
  • How do you write the equation of a line given its slope and y-intercept?
    Use the slope-intercept form: \(y=mx+b\), where m is slope and b is y-intercept.
  • What is the standard form of a linear equation?
    The standard form is \(Ax+By=C\), where A, B, and C are integers and A ≥ 0.