N/A — Exam

Question 36 • Algebra II

If f of x is equal to negative x squared plus 3 x plus 5 and g of x is equal to x squared plus 2 x , which graph shows the graph of open paren f plus g close paren of x ?

Answer

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. A line is shown. The line crosses the y-axis near y equals 6 and slopes downward from left to right. Arrowheads at both ends indicate the line continues beyond the displayed grid.

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. An upward-opening curve is shown. The curve reaches a lowest point at approximately (negative 1 comma 2). Arrowheads at both ends indicate the curve continues upward beyond the displayed grid.

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. A line is shown. The line crosses the y-axis near y equals 6 and slopes upward from left to right. Arrowheads at both ends indicate the line continues beyond the displayed grid.

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. A downward-opening curve is shown. The curve reaches a highest point at approximately (0.5 comma 5) and crosses the x-axis near x equals negative 1 and x equals 2. Arrowheads at both ends indicate the curve continues downward beyond the displayed grid.

Explanation

Add the functions term by term: (f + g)(x) = (−x² + 3x + 5) + (x² + 2x) = 5x + 5. The x² terms cancel, leaving a line with positive slope, so it rises from left to right. Choice A is the upward-sloping line; its y-intercept is described as near 6, while the calculation gives 5.

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