Question

Y = x - 6x + 8. Find the:

a) Vertex
b) Axis of symmetry
c) X-intercepts
d) y-intercept
e) Maximum or Minimum?
f) Domain
g) Range
h) Increasing
i) Decreasing
j) Points at Infinity

Answer 1

The given function y = -5x + 8 is linear, with a y-intercept of 8, an x-intercept of 1.6, and is decreasing everywhere. It has no vertex, axis of symmetry, or maximum or minimum; the domain and range are all real numbers.

Step-by-step explanation:

The equation given is y = x - 6x + 8, which simplifies to y = -5x + 8. This is a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

• Vertex: Not applicable as this is a linear function, not a quadratic.
• Axis of symmetry: Not applicable for the same reason.
• X-intercepts: Set y to 0 and solve for x, yielding x = 1.6.
• Y-intercept: The y-intercept is the value of y when x is 0, which is 8 in this case.
• Maximum or Minimum: Not applicable as linear functions do not have maximum or minimum points.
• Domain: The domain of a linear function is all real numbers, (-∞, ∞).
• Range: The range is also all real numbers, (-∞, ∞), as the function is not bounded vertically.
• Increasing/Decreasing: The function is decreasing everywhere because the slope is negative (-5).
• Points at Infinity: This concept does not typically apply to linear equations in the way it might for rational functions or certain kinds of limits.