Question

vertical shifts quick check
which statement best shows how the vertical shift affects the parent function ( y = x ) when shifted to ( y = x + 5 )? (1 point)
( y = x + 5 ) will have each point 5 steps higher than ( y = x ).
( y = x + 5 ) will have each point 5 steps to the right of ( y = x ).
( y = x + 5 ) will have each point 5 steps lower than ( y = x ).
( y = x + 5 ) will have each point 5 steps to the left of ( y = x ).

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) + k \), if \( k>0 \), the graph shifts up \( k \) units; if \( k<0 \), it shifts down \( k \) units. Here, the parent function is \( y = x \), and the transformed function is \( y = x + 5 \) (assuming a typo, as \( y=x + 57 \) seems out of place, likely \( y=x + 5 \) for the options). So \( k = 5>0 \), meaning vertical shift up.

Step2: Analyze Each Option

• Option 1 (\( y = x + 5 \) higher): Matches the vertical shift up (each \( y \)-value increases by 5, so points are 5 steps higher).
• Option 2 (right shift): Right shift is horizontal (\( y = f(x - h) \)), not vertical.
• Option 3 (lower): \( k = 5>0 \) is up, not down.
• Option 4 (left shift): Left shift is horizontal (\( y = f(x + h) \)), not vertical.

Answer:

\( y = x + 5 \) will have each point 5 steps higher than \( y = x \). (The correct option among the given, likely the first option with \( y = x + 5 \) and "5 steps higher")