Question

If the graph of the function f defined by h left parenthesis x right parenthesis equals x squared plus 3 is translated vertically downward by 2 units, it becomes the graph of a function k. Find the expression for k left parenthesis x right parenthesis.

Group of answer choices

k left parenthesis x right parenthesis equals x squared plus 1

k left parenthesis x right parenthesis equals left parenthesis x plus 2 right parenthesis squared plus 3

k left parenthesis x right parenthesis equals x squared plus 5

k left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis squared plus 3

Answer 1

The function k(x), which represents the graph of h(x) = x² + 3 translated vertically downward by 2 units, is expressed as k(x) = x² + 1.

Step-by-step explanation:

If the graph of the function h(x) = x² + 3 is translated vertically downward by 2 units, it becomes the graph of the function k.

To achieve this translation, we simply subtract 2 from the original function's value. This operation does not change the shape of the graph, only its position along the y-axis. Therefore, the expression for k(x) is:

k(x) = x² + 3 - 2

When we simplify the equation, we see that the expression for k(x) is:

k(x) = x² + 1