Domain and Range of Functions 1

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Question 1 of 4

1. Question
Find the domain and range of $y = 2 x - 1$ $y=2x-1$
- 1. Domain: All positive numbers ; Range: All positive numbers
- 2. Domain: All real numbers; Range: All real numbers
- 3. Domain: All whole numbers ; Range: All whole numbers
- 4. Domain: $2$ $2$ ; Range: $- 1$ $-1$
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The domain and range is the set of $x$ $x$ and $y$ $y$ values of a function

Notice that the line on the graph extends infinitely

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This means that the line will cover all real values of $x$ $x$ and $y$ $y$

$Domain: All real numbers$ $\text(Domain: All real numbers)$

$Range: All real numbers$ $\text(Range: All real numbers)$
Question 2 of 4

2. Question
Find the domain and range of $y = x^{2} + 1$ $y=x^2+1$
- 1. Domain: $x \geq 1$ $x≥1$ ; Range: $y \geq 1$ $y≥1$
- 2. Domain: $x \geq 1$ $x≥1$ ; Range: All real numbers
- 3. Domain: All real numbers; Range: All real numbers
- 4. Domain: All real numbers; Range: $y \geq 1$ $y≥1$
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The domain and range is the set of $x$ $x$ and $y$ $y$ values of a function

Notice that the curve extends infinitely on both sides of the x-axis and has a minimum point at $y = 1$ $y=1$

This means that the curve will cover all real values of $x$ $x$ and all real values of $y$ $y$ greater than or equal to $1$ $1$

$Domain: All real numbers$ $\text(Domain: All real numbers)$

$Range : y \geq 1$ $\text(Range):y≥1$
Question 3 of 4

3. Question
Find the domain and range of $y = - \sqrt{9 - x^{2}}$ $y=-sqrt(9-x^2)$
- 1. Domain: $- 3 \leq x \leq 3$ $-3≤x≤3$ ; Range: $- 3 \leq y \leq 0$ $-3≤y≤0$
- 2. Domain: $- 3 \geq x \geq 3$ $-3≥x≥3$ ; Range: $- 3 \geq y \geq 0$ $-3≥y≥0$
- 3. Domain: $3 \geq x \geq - 3$ $3≥x≥-3$ ; Range: $3 \leq y \leq - 3$ $3≤y≤-3$
- 4. Domain: $3 \leq x \leq - 3$ $3≤x≤-3$ ; Range: $0 \leq y \leq - 3$ $0≤y≤-3$
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The domain and range is the set of $x$ $x$ and $y$ $y$ values of a function

Notice that the curve starts at the x-axis at $x = - 3$ $x=-3$ , curves down to $y = - 3$ $y=-3$ and goes back to the x-axis at $x = 3$ $x=3$

This means that the curve will cover all real values of $x$ $x$ greater than or equal to $- 3$ $-3$ and less than or equal to $3$ $3$ and all real values of $y$ $y$ greater than or equal to $- 3$ $-3$ and less than or equal to $0$ $0$

$Domain : - 3 \leq x \leq 3$ $\text(Domain):-3≤x≤3$

$Range : - 3 \leq y \leq 0$ $\text(Range):-3≤y≤0$
Question 4 of 4

4. Question
Find the domain and range of $y = 2 x + 2$ $y=2x+2$
- 1. Domain: $1 \leq x \leq - 1$ $1≤x≤-1$ ; Range: $3 \leq y \leq 1$ $3≤y≤1$
- 2. Domain: $- 1 \geq x \geq 1$ $-1≥x≥1$ ; Range: $1 \geq y \geq 3$ $1≥y≥3$
- 3. Domain: $- 1 \leq x \leq 1$ $-1≤x≤1$ ; Range: $1 \leq y \leq 3$ $1≤y≤3$
- 4. Domain: $- 1 \leq x \leq 1$ $-1≤x≤1$ ; Range: $1 \geq y \geq 3$ $1≥y≥3$
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The domain and range is the set of $x$ $x$ and $y$ $y$ values of a function

Notice that the line starts at the point $(- 1, 1)$ $(-1,1)$ and ends at point `(1,3)“

This means that the line will cover all real values of $x$ $x$ greater than or equal to $- 1$ $-1$ and less than or equal to $1$ $1$ and all real values of $y$ $y$ greater than or equal to $1$ $1$ and less than or equal to $3$ $3$

$Domain : - 1 \leq x \leq 1$ $\text(Domain):-1≤x≤1$

$Range : 1 \leq y \leq 3$ $\text(Range):1≤y≤3$

Domain and Range of Functions 1

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