The equation for the final transformed graph is:
f(x) = x - 1, if x ≥ -6
-x - 4, if x < -6
To find the equation for the final transformed graph, we need to apply the given transformations to the function f(x) = |x| in the given order. The transformations are:
Shift 3 units to the left
Shift downward 4 units
To shift the graph 3 units to the left, we need to replace x with (x + 3) in the function. This gives us:
f(x) = |x| → f(x + 3) = |x + 3|
To shift the graph downward 4 units, we need to subtract 4 from the function. This gives us:
f(x + 3) = |x + 3| → f(x + 3) - 4 = |x + 3| - 4
Simplifying the expression |x + 3| - 4, we get:
|x + 3| - 4 =
x + 3 - 4, if x + 3 ≥ 0
-(x + 3) - 4, if x + 3 < 0
Combining the two cases, we get:
f(x + 3) - 4 =
x - 1, if x ≥ -3
-x - 7, if x < -3
Therefore, the equation for the final transformed graph is:
f(x) = x - 1, if x ≥ -6
-x - 4, if x < -6
Complete question:
A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. Given the function f(x) = |x|, shift 3 units to the left and shift downward 4 units.