The graph and equation that represent the same function include:
f(x) = |x| ↔ Graph 3.
f(x) = |x - 5| ↔ Graph 1.
f(x) = |x| - 5 ↔ Graph 5.
f(x) = |x + 5| ↔ Graph 4.
f(x) = |x| + 5 ↔ Graph 2.
In Mathematics, the vertex form of the equation for an absolute value function can be modeled by the following:
y = a|x - h| + k.
Where:
This function, f(x) = |x| represents the parent absolute value function or the standard form of an absolute value function, which is correctly illustrated by graph 3 centered at the origin (0, 0).
This function, f(x) = |x - 5| indicates that the parent absolute value function was horizontally shifted to the right by 5 units, as correctly depicted by graph 1.
This function, f(x) = |x| - 5 indicates that the parent absolute value function was vertically shifted downward by 5 units, as correctly depicted by graph 5.
This function, f(x) = |x + 5| indicates that the parent absolute value function was horizontally shifted to the left by 5 units, as correctly depicted by graph 4.
This function, f(x) = |x| + 5 indicates that the parent absolute value function was vertically shifted upward by 5 units, as correctly depicted by graph 2.