What is the graph of the function rule? y = |4x| – 3 (1 point) Responses Image with alt text: A graph with a V shape opening down. The vertex, or maximum, is at (0, negative 3) and the graph passing through (negative 1, negative 7) and (1, negative 7). Image with alt text: A graph with a V shape opening down. The vertex, or maximum, is at (0, 3) and the graph passing through (negative 1, negative 1) and (1, negative 1). Image with alt text: A graph with a V shape opening up. The vertex, or maximum, is at (0, 3) and the graph passing through (negative 1, 7) and (1, 7).
The correct answer is:
Image with alt text: A graph with a V shape opening up. The vertex, or maximum, is at (0, 3) and the graph passing through (negative 1, 7) and (1, 7).
Answer in ABCD format
The correct answer in ABCD format is D.
To determine the graph of the function y = |4x| - 3, we need to understand the properties of the absolute value function and the effect of transformations on the graph.
The absolute value function |x| gives the distance of x from zero on the number line. Thus, |4x| would give the distance of 4x from zero.
The function rule y = |4x| - 3 subtracts 3 from the distance 4x. This means that the graph will shift downward by 3 units.
Now, let's analyze the options provided:
Option 1: A graph with a V shape opening down, vertex at (0, negative 3), and passing through (-1, -7) and (1, -7).
This option aligns with our analysis so far. The vertex of the graph should be at (0, -3) since the graph shifted downward by 3 units. Additionally, the graph opening down matches the behavior of the absolute value function.
Option 2: A graph with a V shape opening down, vertex at (0, 3), and passing through (-1, -1) and (1, -1).
This option is incorrect because the vertex is at (0, 3) instead of (0, -3). The sign in front of the 3 is crucial in determining the direction the graph moves.
Option 3: A graph with a V shape opening up, vertex at (0, 3), and passing through (-1, 7) and (1, 7).
This option is incorrect because the graph cannot open up. The absolute value function always results in a V shape that opens either up or down, depending on the sign of the coefficient in front.
Therefore, the correct answer is Option 1: A graph with a V shape opening down, vertex at (0, -3), and passing through (-1, -7) and (1, -7).