Question

● Given the parent functions for linear, exponential, and quadratic
functions, create a graph and state the domain and range for each.

Answer 1

Here are the three parent functions with a short sketch guide, key points to plot, and their domains and ranges.

1) Linear parent: f(x) = x
- How to sketch: draw the x- and y-axes and plot points (−2,−2), (−1,−1), (0,0), (1,1), (2,2). Connect them with a straight line through the origin with slope 1.
- Domain: (−∞, ∞)
- Range: (−∞, ∞)

2) Exponential parent: f(x) = 2^x (typical exponential parent)
- How to sketch: draw axes, plot (−2, 0.25), (−1, 0.5), (0,1), (1,2), (2,4). The curve passes through (0,1) and increases rapidly for x > 0; it approaches y = 0 as x → −∞ (horizontal asymptote at y = 0) but never touches it.
- Domain: (−∞, ∞)
- Range: (0, ∞)

3) Quadratic parent: f(x) = x^2
- How to sketch: draw axes, plot (−2,4), (−1,1), (0,0), (1,1), (2,4). Connect with a smooth U-shaped parabola opening upward with vertex at (0,0).
- Domain: (−∞, ∞)
- Range: [0, ∞)

If you want, I can produce an actual plotted image (PNG/SVG) of all three on one coordinate plane.