Questions: Graph the following function on the axes provided. f(x) = - -x-3 for x<1 - 2 for x=1 - 6x-7 for x>1

Solution Steps

For \( x < 1 \), the function is \( f(x) = -x - 3 \). This is a linear function with a slope of -1 and a y-intercept of -3.

To graph this:

• Start at the y-intercept (0, -3).
• Use the slope to find another point. For example, from (0, -3), move down 1 unit and right 1 unit to get to the point (1, -4).
• Since this part of the function is only valid for \( x < 1 \), draw the line up to but not including \( x = 1 \). Use an open circle at \( x = 1 \) to indicate that this point is not included.

For \( x = 1 \), the function is \( f(x) = 2 \).

To graph this:

• Plot a closed circle at the point (1, 2) to indicate that this point is included in the function.

For \( x > 1 \), the function is \( f(x) = 6x - 7 \). This is a linear function with a slope of 6 and a y-intercept of -7.

To graph this:

• Start at the y-intercept (0, -7).
• Use the slope to find another point. For example, from (0, -7), move up 6 units and right 1 unit to get to the point (1, -1).
• Since this part of the function is only valid for \( x > 1 \), draw the line starting just after \( x = 1 \). Use an open circle at \( x = 1 \) to indicate that this point is not included.

Final Answer