For each function, state whether it is linear, quadratic, or exponential. Function 1 Function 2 Function 3 x y x y x y 3 35 1 9 2 -8 4 25 2 7 3 -16 5 18 3 9 4 -24 6 14 bar(4) 15 bar(5) 7 13 sqrt5 25 bar(6) -40 Linear Linear Linear Quadratic Quadratic Quadratic Exponential Exponential Exponential None of the above None of the above None of the above

Analyze Function 1: Analyze Function 1 by checking the differences in y-values as x increases by 1. Calculate the differences: 35-25=10, 25-18=7, 18-14=4, 14-13=1. Identify Quadratic Pattern: Notice the differences between consecutive y-values are decreasing, suggesting a non-linear pattern. Check second differences: 7-10=-3, 4-7=-3, 1-4=-3. Analyze Function 2: Since the second differences are constant, Function 1 is quadratic. No Consistent Pattern: Analyze Function 2 by checking the y-values directly given the x-values. Notice y-values: 9, 7, 9, 15, 25. Analyze Function 3: Observe that y-values do not follow a consistent pattern of change, either linear or quadratic. Check for exponential pattern by ratios: 7/9, 9/7. Identify Pattern: Ratios are not consistent, indicating Function 2 is neither linear, quadratic, nor exponential. Analyze Function 3 by checking the y-values. Notice y-values: -8, -16, -24, -40. Calculate the differences: -16 - (-8) = -8, -24 - (-16) = -8, -40 - (-24) = -16.

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For each function, state whether it is linear, quadratic, or exponential.

Function 1
Function 2
Function 3

x

y

x

y

x

y

3
35
1
9
2
-8

4
25
2
7
3
-16

5
18
3
9
4
-24

6
14

bar(4)
15

bar(5)

7
13

sqrt5
25

bar(6)
-40

Linear
Linear
Linear

Quadratic
Quadratic
Quadratic

Exponential
Exponential
Exponential

None of the above
None of the above
None of the above

For each function, state whether it is linear, quadratic, or exponential. $\newline$ $\newline$ Function $1$ $\newline$ Function $2$ $\newline$ Function $3$ $\newline$ $\newline$ $x$ $\newline$ $y$ $\newline$ $x$ $\newline$ $y$ $\newline$ $x$ $\newline$ $y$ $\newline$ $\newline$ $3$ $\newline$ $35$ $\newline$ $1$ $\newline$ $9$ $\newline$ $y$ $0$ $\newline$ $y$ $1$ $\newline$ $\newline$ $y$ $2$ $\newline$ $y$ $3$ $\newline$ $y$ $0$ $\newline$ $y$ $5$ $\newline$ $3$ $\newline$ $y$ $7$ $\newline$ $\newline$ $y$ $8$ $\newline$ $y$ $9$ $\newline$ $3$ $\newline$ $9$ $\newline$ $y$ $2$ $\newline$ $x$ $3$ $\newline$ $\newline$ $x$ $4$ $\newline$ $x$ $5$ $\newline$ \bar{ $4$ }$\newline$$x$$6$$\newline$\bar{$5$} $\newline$ $\newline$ $y$ $5$ $\newline$ $x$ $8$ $\newline$ $x$ $9$ $\newline$ $y$ $3$ $\newline$ \bar{ $6$ }$$\newline$$y$$1$$\newline$$\newline$Linear$\newline$Linear$\newline$Linear$\newline$Quadratic$\newline$Quadratic$\newline$Quadratic$\newline$Exponential$\newline$Exponential$\newline$Exponential$\newline$None of the above$\newline$None of the above$\newline$None of the above

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Math Problems

Algebra 1

Domain and range of quadratic functions: equations

Full solution

Q. For each function, state whether it is linear, quadratic, or exponential.

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1

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9

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x

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Analyze Function $1$ : Analyze Function $1$ by checking the differences in y-values as $x$ increases by $1$ . Calculate the differences: $35-25=10$ , $25-18=7$ , $18-14=4$ , $14-13=1$ .
Identify Quadratic Pattern: Notice the differences between consecutive $y$ -values are decreasing, suggesting a non-linear pattern. Check second differences: $7-10=-3$ , $4-7=-3$ , $1-4=-3$ .
Analyze Function $2$ : Since the second differences are constant, Function $1$ is quadratic.
No Consistent Pattern: Analyze Function $2$ by checking the $y$ -values directly given the $x$ -values. Notice $y$ -values: $9$ , $7$ , $9$ , $15$ , $25$ .
Analyze Function $3$ : Observe that $y$ -values do not follow a consistent pattern of change, either linear or quadratic. Check for exponential pattern by ratios: $\frac{7}{9}$ , $\frac{9}{7}$ .
Identify Pattern: Ratios are not consistent, indicating Function $2$ is neither linear, quadratic, nor exponential.
Identify Pattern: Ratios are not consistent, indicating Function $2$ is neither linear, quadratic, nor exponential. Analyze Function $3$ by checking the $y$ -values. Notice $y$ -values: $-8$ , $-16$ , $-24$ , $-40$ .
Identify Pattern: Ratios are not consistent, indicating Function $2$ is neither linear, quadratic, nor exponential. Analyze Function $3$ by checking the $y$ -values. Notice $y$ -values: $-8$ , $-16$ , $-24$ , $-40$ . Calculate the differences: $-16 - (-8) = -8$ , $-24 - (-16) = -8$ , $-40 - (-24) = -16$ .