Question

analyzing a relationship between functions
justine graphs the function ( f(x) = (x - 7)^2 - 1 ). on the same grid, she graphs the function ( g(x) = (x + 6)^2 - 3 ). which transformation will map ( f(x) ) on to ( g(x) )?

• left 13 units, down 2 units
• right 13 units, down 2 units
• left 13 units, up 2 units
• right 13 units, up 2 units

Explanation:

Step1: Identify vertex of $f(x)$

Vertex form: $f(x)=(x-h)^2+k$. For $f(x)=(x-7)^2-1$, vertex is $(7, -1)$.

Step2: Identify vertex of $g(x)$

For $g(x)=(x+6)^2-3=(x-(-6))^2-3$, vertex is $(-6, -3)$.

Step3: Calculate horizontal shift

Find difference in $x$-coordinates: $-6 - 7 = -13$. Negative = left 13 units.

Step4: Calculate vertical shift

Find difference in $y$-coordinates: $-3 - (-1) = -2$. Negative = down 2 units.

Answer:

left 13 units, down 2 units