Question

The values on both axes range from negative 4 to 4 in increments of 1. The dotted line, labeled Option 1, begins in quadrant 3 sloping upward from left to right, passes through quadrant 4, and then rises through quadrant 1. The dotted line passes through left parenthesis negative 3 comma negative 4 right parenthesis and left parenthesis 4 comma 3 right parenthesis. The dashed line, labeled Option 2, begins in quadrant 2 sloping downward from left to right, passes through quadrant 3, and then descends through quadrant 4. The dashed line passes through left parenthesis negative 4 comma 3 right parenthesis and left parenthesis 3 comma negative 4 right parenthesis. The dot-dashed line, labeled Option 3, begins in quadrant 2 sloping downward from left to right, passes through quadrant 1, and then descends through quadrant 4. The dot-dashed line passes through left parenthesis negative 3 comma 4 right parenthesis and left parenthesis 4 comma negative 3 right parenthesis. The solid line, labeled Option 4 f left parenthesis x right parenthesis equals to x plus 1, begins in quadrant 3 sloping upward from left to right, passes through quadrant 2, and then rises through quadrant 1. The solid line passes through left parenthesis negative 4 comma negative 3 right parenthesis and left parenthesis 3 comma 4 right parenthesis.

Given the graph of f(x)=x+1 , which of the options is the graph of −f(x) ?

(1 point)

Option 2

Option 1

Option 3

Option 4

Answer 1

Option 2.

Reason: −f(x) = −(x+1) = −x − 1 has slope −1 and y-intercept −1. The dashed line (Option 2) passes through (−4, 3) and (3, −4), and for x = −4 and x = 3, −x − 1 gives 3 and −4 respectively, so it matches.