Question

1. both of these functions grow as x gets larger and larger. which function eventually exceeds the other?

$f(x) = 4.5x^{2}$
$g(x) = 6x + 2$
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1. is this function linear, quadratic, or exponential?

x	y
-9	24
-8	21
-7	18
-6	15
-5	12

linear
quadratic
exponential

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questions answered 7
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algebra 1 > aa.4 identify linear, quadratic, and

Explanation:

First Question:

Step1: Compare function growth rates

Quadratic functions ($f(x)=4.5x^2$) grow faster than linear functions ($g(x)=6x+2$) as $x\to\infty$.

Step2: Verify with large $x$

Let $x=100$: $f(100)=4.5(100)^2=45000$, $g(100)=6(100)+2=602$. $45000>602$.

Step1: Check first differences of $y$

$\Delta y_1=24-21=3$, $\Delta y_2=21-18=3$, $\Delta y_3=18-15=3$, $\Delta y_4=15-12=3$

Step2: Identify function type

Constant first differences mean linear function.

Answer:

$f(x) = 4.5x^2$ eventually exceeds $g(x) = 6x + 2$

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Second Question: