Question

the graph of y = f(x) is the solid black graph below. which function represents the dotted graph? answer y = f(x + 5) - 4 y = f(x - 5) - 4 y = f(x - 5) + 4 y = f(x + 5) + 4 submit answer

Explanation:

Step1: Recall transformation rules

For a function $y = f(x)$, a horizontal shift of $h$ units and a vertical shift of $k$ units is given by $y=f(x - h)+k$. A left - shift is when $h<0$ and a right - shift is when $h > 0$. A down - shift is when $k<0$ and an up - shift is when $k>0$.

Step2: Analyze horizontal shift

The dotted graph is shifted 5 units to the left of the solid graph. For a left - shift of 5 units, in the formula $y = f(x - h)+k$, we have $h=- 5$. So the function becomes $y = f(x+5)$.

Step3: Analyze vertical shift

The dotted graph is shifted 4 units down from the solid graph. For a down - shift of 4 units, $k=-4$. So the function is $y=f(x + 5)-4$.

Answer:

$y = f(x + 5)-4$