Question

Use the images to answer the question.

Original function:

A coordinate plane's x-axis ranges from negative 9 to 9 and its y-axis ranges from negative 11 to 11, both by 1-unit increments. A concave up parabola labeled f of x equals x squared is plotted passing through 7 marked points.
▼Click for Long Desc
The marked points are located as follows: left parenthesis 3 comma 9 right parenthesis, left parenthesis 2 comma 4 right parenthesis, left parenthesis 1 comma 1 right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis negative 1 comma 1 right parenthesis, left parenthesis negative 2 comma 4 right parenthesis, and left parenthesis negative 3 comma 9 right parenthesis.

Translated function:

A coordinate plane's x-axis ranges from negative 9 to 9 and its y-axis ranges from negative 11 to 11, both by 1-unit increments. A parabola of the function f left parenthesis x parenthesis is plotted.
▼Click for Long Desc
The function f left parenthesis x parenthesis is equal to left parenthesis x plus 1 right parenthesis squared. The parabola passes through the following marked points: left parenthesis negative 4 comma 9 right parenthesis, left parenthesis negative 3 comma 4 right parenthesis, left parenthesis negative 2 comma 1 right parenthesis, left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma 1 right parenthesis, left parenthesis 1 comma 4 right parenthesis, and left parenthesis 2 comma 9 right parenthesis.

Notice the horizontal shift in the images.
What is the value of k for the horizontal shift that occurred between the graph of the original function y=f(x)
and the graph of the translated function y=f(x−k)
?

(1 point)

Answer 1

k = −1

Reason: f(x−k) = (x−k)^2 = (x+1)^2, so −k = 1 → k = −1, a shift 1 unit left.