Question

Write the equation of the function. Use function notation.

Answer 1

Answer: $f(x) = \left \{ {{x + 3---->; x }\leq 2 \atop {-x+7---->; x}\geq2 } \right.$

Step-by-step explanation:

Left line:

slope (m) = 1 and y - intercept (b) = 3

equation in slope-intercept (y = mx + b) format is: y = x + 3

this line exists only when x ≤ 2

Right line:

a point on the line = (2, 5) and slope (m) = -1

equation in point-slope [y - y₁ = m(x - x₁)] format is: y - 5 = -(x - 2)

convert that to slope-intercept format: y = -x + 2 + 5  ⇒  y = -x + 7

this line only exists when x ≥ 2

$f(x) = \left \{ {{x + 3---->; x }\leq 2 \atop {-x+7---->; x}\geq2 } \right.$