Questions: Sketch the graph of g(x) = - x + 2 if x < 2 - -4 if x ≥ 2

Solution Steps

The given function is a piecewise function defined as: \[ g(x) = \begin{cases} -x + 2 & \text{if } x \leq 2 \\ -4 & \text{if } x > 2 \end{cases} \]

For \( x \leq 2 \), the function is \( g(x) = -x + 2 \). This is a linear function with a slope of -1 and a y-intercept of 2.

• When \( x = 2 \), \( g(2) = -2 + 2 = 0 \).
• When \( x = 0 \), \( g(0) = -0 + 2 = 2 \).
• When \( x = -2 \), \( g(-2) = -(-2) + 2 = 4 \).

Plot these points and draw a line through them, extending to the left.

For \( x > 2 \), the function is \( g(x) = -4 \). This is a constant function.

• For any \( x > 2 \), \( g(x) = -4 \).

Draw a horizontal line at \( y = -4 \) starting from \( x = 2 \) and extending to the right.

Final Answer