Which is the graph of f of x is equal to absolute value of x reflected across the x -axis, translated 3 units left, 4 units up, and dilated by a factor of 4 ?
Answer
A
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening downward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 7 comma 0) and (1 comma 0).
B
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening downward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 4 comma 0) and (negative 2 comma 0).
C
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening upward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 4 comma 8) and (negative 2 comma 8).
D
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening upward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 6 comma 7) and (0 comma 7).
Explanation
Reflecting y = |x| across the x-axis gives y = -|x|. Shifting 3 units left and 4 units up gives y = -|x + 3| + 4; a dilation by a factor of 4 makes it y = -4|x + 3| + 4. Its vertex is (-3, 4), and at x = -4 or -2 its value is 0, so the graph opens downward and passes through (-4, 0) and (-2, 0).
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