Determine the relationship described in each table. Please help me
1 answer:
I graphed the given points and based on my graph.
<span> x y </span>→ EXPONENTIAL<span><span>
</span> <span> -2 21
</span><span> 1 4
</span><span> 0 1
</span><span> 1 0
</span></span><span> x y </span>→ LINEAR<span><span>
</span> <span> -2 6
</span> <span> -1 -2
</span><span> 0 2
</span><span> 1 6
</span></span>
<span> x y </span>→ QUADRATIC<span><span>
</span> <span> -2 12
</span> <span> -1 -2
</span><span> 0 -8
</span><span> 1 -6
</span></span><span> <span><span> x y </span></span></span>→ EXPONENTIAL<span><span><span>
</span> <span> -2 16
</span> <span> -1 8
</span><span> 0 4
</span><span> 1 2
LINEAR FUNCTIONS always maintain a constant slope. In the above linear function, the slope is 4.
EXPONENTIAL and QUADRATIC FUNCTIONS have different slope in every point.
Exponential functions can be identified by the immediate increase or decrease in the value of y resulting to a minimal increase or decrease in the value of x.
Quadratic functions can be identified as such due to the similar points it has after having the vertex.
</span></span></span>
<span> x y </span>→ EXPONENTIAL<span><span>
</span> <span> -2 21
</span><span> 1 4
</span><span> 0 1
</span><span> 1 0
</span></span><span> x y </span>→ LINEAR<span><span>
</span> <span> -2 6
</span> <span> -1 -2
</span><span> 0 2
</span><span> 1 6
</span></span>
<span> x y </span>→ QUADRATIC<span><span>
</span> <span> -2 12
</span> <span> -1 -2
</span><span> 0 -8
</span><span> 1 -6
</span></span><span> <span><span> x y </span></span></span>→ EXPONENTIAL<span><span><span>
</span> <span> -2 16
</span> <span> -1 8
</span><span> 0 4
</span><span> 1 2
LINEAR FUNCTIONS always maintain a constant slope. In the above linear function, the slope is 4.
EXPONENTIAL and QUADRATIC FUNCTIONS have different slope in every point.
Exponential functions can be identified by the immediate increase or decrease in the value of y resulting to a minimal increase or decrease in the value of x.
Quadratic functions can be identified as such due to the similar points it has after having the vertex.
</span></span></span>
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The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"
<h3>What is the explanation for the above?</h3>- Lets examine f(x) = 3x + 14
Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.
- Let us examine h(x) = 3ˣ + 1
This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:
y = 0
- Let us look at F'(x) = Log₃ (x = 1).
This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0
- Let us take a look at g(x) = X⁴ + 3x² - 14
Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.
Learn more about functions:
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