Question

homework assignment 1.1: functions and function notation
score: 8/15 answered: 8/15
question 9
match each function name with its equation.
$y = x$
$y = x^2$
$y = \sqrt3{x}$
$y = \sqrt{x}$
$y = x^3$
$y = \frac{1}{x^2}$
$y = |x|$
$y = \frac{1}{x}$
a. cube root
b. reciprocal
c. reciprocal squared
d. square root
e. absolute value
f. linear
g. cubic
h. quadratic

Explanation:

• For \( y = x \), it's a linear function (form \( y = mx + b \) with \( m = 1, b = 0 \)), so matches f.
• \( y = x^2 \) is a quadratic function (degree 2), matches h.
• \( y=\sqrt[3]{x} \) is the cube root function, matches a.
• \( y = \sqrt{x} \) is the square root function, matches d.
• \( y = x^3 \) is a cubic function (degree 3), matches g.
• \( y=\frac{1}{x^2} \) is the reciprocal squared function, matches c.
• \( y = |x| \) is the absolute value function, matches e.
• \( y=\frac{1}{x} \) is the reciprocal function, matches b.

Answer:

• \( y = x \): f. Linear
• \( y = x^2 \): h. Quadratic
• \( y=\sqrt[3]{x} \): a. Cube root
• \( y = \sqrt{x} \): d. Square Root
• \( y = x^3 \): g. Cubic
• \( y=\frac{1}{x^2} \): c. Reciprocal Squared
• \( y = |x| \): e. Absolute Value
• \( y=\frac{1}{x} \): b. Reciprocal