Graphs of Parent Functions

(a) Constant Function
A horizontal line labeled f(x) = c is graphed on the x y-coordinate plane. The line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 1.25, continues horizontally right, and exits the window in the first quadrant.
(b) Identity Function
A line labeled f(x) = x is graphed on the x y-coordinate plane. The line enters the window in the third quadrant, goes up and right, passes through the point (−1, −1), crosses the x-axis at the origin, passes through the point (1, 1), and exits the window in the first quadrant.
(c) Absolute Value Function
A function labeled f(x) = |x| is graphed on the x y-coordinate plane. The function enters the window in the second quadrant, goes down and right, passes through the point (−1, 1), changes direction at the origin, goes up and right, passes through the point (1, 1), and exits the window in the first quadrant.
(d) Square Root Function
A curve labeled f(x) = √(x) is graphed on the x y-coordinate plane. The curve begins at the origin, goes up and right becoming less steep, passes through the point (1, 1), and exits the window in the first quadrant.
(e) Squaring Function
A curve labeled f(x) = x2 is graphed on the x y-coordinate plane. The curve enters the window in the second quadrant, goes down and right becoming less steep, passes through the point (−1, 1), changes direction at the origin, goes up and right becoming more steep, passes through the point (1, 1), and exits the window in the first quadrant.
(f) Cubic Function
A curve labeled f(x) = x3 is graphed on the x y-coordinate plane. The curve enters the window in the third quadrant, goes up and right becoming less steep, passes through the point (−1, −1), becomes nearly horizontal as it crosses the origin, goes up and right becoming more steep, passes through the point (1, 1), and exits the window in the first quadrant.
(g) Reciprocal Function
A curve with 2 parts labeled f(x) = 1 ⁄ x is graphed on the x y-coordinate plane. The first part of the curve enters the window nearly horizontal below the negative x-axis, goes down and right becoming more steep, passes through the point (−2, −0.5), passes through the point (−1, −1), and exits the window nearly vertical to the left of the negative y-axis. The second part of the curve enters the window nearly vertical to the right of the positive y-axis, goes down and right becoming less steep, passes through the point (1, 1), passes through the point (2, 0.5), and exits the window nearly horizontal above the positive x-axis.
(h) Greatest Integer Function
A function with 6 parts labeled f(x) = [[x]] is graphed on the x y-coordinate plane. All 6 parts are horizontal line segments that begin with a closed point and end with an open point. The starting and ending points of each part is as follows.
  • The first part starts at (−3, −3) and ends at (−2, −3).
  • The second part starts at (−2, −2) and ends at (−1, −2).
  • The third part starts at (−1, −1) and ends at (0, −1).
  • The fourth part starts at (0, 0) and ends at (1, 0).
  • The fifth part starts at (1, 1) and ends at (2, 1).
  • The sixth part starts at (2, 2) and ends at (3, 2).