Questions: Graph this function. f(x)= x+5 if x<1 6x-12 if x ≥ 1

Transcript text: Graph this function. \[ f(x)=\left\{\begin{array}{ll} x+5 & \text { if } x<1 \\ 6 x-12 & \text { if } x \geq 1 \end{array}\right. \]

Solution

Solution Steps

Step 1: Analyze the first equation

The first equation is f(x) = x + 5 if x < 1. We need two points to graph this. Let's choose x = 0 and x = -1.

If x = 0, f(x) = 0 + 5 = 5. This gives the point (0, 5). If x = -1, f(x) = -1 + 5 = 4. This gives the point (-1, 4).

Since x is strictly less than 1, there will be an open circle at x = 1. When x = 1, f(x) = 1 + 5 = 6. Thus, there's an open circle at (1, 6).

Step 2: Analyze the second equation

The second equation is f(x) = 6x - 12 if x ≥ 1. Let's choose x = 1 and x = 2.

If x = 1, f(x) = 6(1) - 12 = 6 - 12 = -6. This gives the point (1, -6). If x = 2, f(x) = 6(2) - 12 = 12 - 12 = 0. This gives the point (2, 0).

Since x is greater than or equal to 1, there will be a closed circle at x = 1.