Math Problem Statement

f(x)=−(x−5) y coordiante of the y intecerpt of the polynomial function defined below.

Solution

To determine the y-coordinate of the y-intercept of the function f(x)=(x5)f(x) = -(x - 5), we evaluate f(x)f(x) at x=0x = 0, since the y-intercept occurs where x=0x = 0.

Step-by-Step Solution:

  1. The function is given as: f(x)=(x5)f(x) = -(x - 5)
  2. Substituting x=0x = 0: f(0)=(05)f(0) = -(0 - 5)
  3. Simplify the expression: f(0)=(5)f(0) = -(-5)
  4. Therefore: f(0)=5f(0) = 5

Final Answer:

The y-coordinate of the y-intercept is 5.


Would you like further clarification or additional examples? Here are some related questions to explore:

  1. What is the x-coordinate of the x-intercept of this function?
  2. How do you find intercepts for quadratic functions?
  3. How does the slope of a linear function like this affect its graph?
  4. Can you rewrite this function in slope-intercept form?
  5. How would this function change if the negative sign were removed?

Tip: Always evaluate the y-intercept by substituting x=0x = 0 into the function!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Intercepts

Formulas

y-intercept: f(0)

Theorems

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Suitable Grade Level

Grades 6-8