Asked by C.W

The values on the x-axis range from negative 7 to 7 in increments of 1. The values on the y-axis range from negative 4 to 4 in increments of 1. A solid wave plotted in quadrant 2 is labeled f left parenthesis x right parenthesis equals sine x plus 2. The solid wave passes through left parenthesis negative 6.3 comma 2 right parenthesis, left parenthesis negative 4.5 comma 3 right parenthesis, left parenthesis negative 1.5 comma 1 right parenthesis, and left parenthesis 0 comma 2 right parenthesis. A dotted wave plotted in quadrant 3 is labeled Option 1. The dotted wave passes through left parenthesis negative 6.3 comma negative 2 right parenthesis, left parenthesis negative 4.8 comma negative 3 right parenthesis, left parenthesis negative 1.5 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 2 right parenthesis. A dashed wave plotted in quadrant 4 is labeled Option 2. The dashed wave passes through left parenthesis 0 comma negative 2 right parenthesis, left parenthesis 1.5 comma negative 1 right parenthesis, left parenthesis 4.5 comma negative 3 right parenthesis, and left parenthesis 6.3 comma negative 2 right parenthesis. A dot-dashed wave plotted in quadrant 1 is labeled Option 3. The dot-dashed wave passes through left parenthesis 0 comma 2 right parenthesis, left parenthesis 1.5 comma 1 right parenthesis, left parenthesis 4.5 comma 3 right parenthesis, and left parenthesis 6.3 comma 2 right parenthesis. A dot-dot-dashed wave plotted in quadrants 2 and 3 is labeled Option 4. This solid wave passes through left parenthesis negative 6.3 comma 0 right parenthesis, left parenthesis negative 4.5 comma negative 1 right parenthesis, left parenthesis negative 1.5 comma 1 right parenthesis, and left parenthesis 0 comma 0 right parenthesis. All values are approximate.

Describe the transformation of the graph of f(x)=sinx+2
to the graph labeled Option 2.

(1 point)

Option 2 is the graph of −f(x)
.

Option 2 is the graph of f(−x)
.

Option 2 is the graph of f(x−7)
.

Option 2 is the graph of −f(−x)
.

All Answers 1

Answered by GPT-5 mini AI
- f(-x)

Explanation: f(x)=sin x+2 has f(0)=2 and f(-1.5)=1. Reflecting across the y-axis gives f(-x) with points (0,2) and (1.5,1). Then reflecting across the x-axis (negating the y-values) gives -f(-x) with points (0,-2) and (1.5,-1), which match Option 2.