THE PARENT FUNCTION GRAPHS AND TRANSFORMATIONS!

Mashup Math2 minutes read

The constant function f(x) = 5 is a horizontal line, the linear function f(x) = x is a diagonal line with a slope of one, and the absolute value function f(x) = |x| remains above the x-axis, starting at zero and moving up to positive infinity.

Insights

  • The constant function f(x) = 5 is a horizontal line with a range of 5 and a domain extending from negative to positive infinity.
  • The absolute value function f(x) = |x| is always non-negative, starting at zero and moving up to positive infinity, with a domain from negative infinity to positive infinity.

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Recent questions

  • Define constant function in mathematics?

    A function with a fixed output value.

  • Explain linear function characteristics?

    A function with a constant slope and y-intercept.

  • What is an absolute value function?

    A function that returns the distance from zero.

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Summary

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Functions and their graphical representations

  • The constant function, f(x) = 5, represents a horizontal line with a domain from negative infinity to positive infinity and a range of 5.
  • The linear function, f(x) = x, forms a diagonal line with a slope of one and a y-intercept of zero, having a domain and range from negative infinity to positive infinity.
  • The absolute value function, f(x) = |x|, remains above the x-axis with a domain of negative infinity to positive infinity and a range starting at zero and moving up to positive infinity, never negative.
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