Here is a list of numbers: 7.3, 4.2, 7.3, 6.7, 4.2, 9.3, 1.2 ,1.1 ,6.4 ,8 State the median.
1 answer:
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Answer:
Zeros : 1 , -1, 3
Degree : 4
End Behaviour : At x-> ∞ f(x) -> ∞ and x->-∞ f(x) -> ∞
Y - intercept : -3
Extra Points: (0,-3), (2,-3)
Step-by-step explanation:
f(x) = 0 to find the zeros
Clearly x = -1,1,3
Here 1 is a repeating root as it is (x-1)²
Degree is highest power of x in f(x)
Clearly it is x*x²*x = x⁴ is the maximum power of x
Thus degree is 4
Looking at end behavior we substitute x->∞ and x-> -∞
Clearly f(x)>0 as all terms are positive and f(x)->∞
Similarly when x->-∞
f(x)>0 as 2 terms are -ve and their product is positive thus f(x)-> ∞
Y-Intercept is f(0)
f(0) = (0+1)(0-1)²(0-3) = 1*1*-3 = -3
Thus Y-Intercept is -3
Substitute x = 0 , 2 for extra points
Thus f(0) = -3
and f(2) = -3
Thus points on the graph (0,-3), (0,2)
We can use all this information to draw a graph remember that 1 is a repeating root so that will be a point of minima. The graph is a parabola that passes through x-axis at x = -1, 3.
Considering the definition of map and scale, an actual distance of 269.59 km represent a scale distance of 5.7 inches .
<h3>Definition of map and scale</h3>A map is a representation of a place, at a size smaller than the real size.
The scale of a cartographic representation is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. That is, the scale is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.
One way to represent the scale is by a fraction, which indicates the proportion between the distance on a map and its corresponding distance in reality:
In this case, you know that a scale distance of 3.5 inches on a map represent an actual distance of 175 km.
To know the real distance that represents a scale distance of 5.7 inches, as the scale ratio is the same as in the previous case, it is expressed:
Solving:
×distance in reality= 5.7 inches
distance in reality=
<u><em>distance in reality= 269.59 km</em></u>
In summary, an actual distance of 269.59 km represent a scale distance of 5.7 inches .
Learn more about map and scale:
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Range is set of all y-values. To find a range of graphed function, we need to know that range starts from the minimum value of graph to maximum value. That's because the minimum value is the least value that you can get by substituting the domain and the maximum value is the largest value that you can get by substituting the domain as well.
Now we don't talk about domain here, we talk about range. See the attachment! You are supposed to focus on y-axis, plane or vertical line. See how the minimum value of function is the negative value while the maximum value is positive.
That means any ranges that don't contain the negative values are cleared out. (Hence A and C choices are wrong.)
Next, range being set of all real numbers mean that graphed functions don't have maximum value or minimum value (We can say that both max and min are infinite.)
Take a look at line graph as an example of range being set of all real numbers, or cubic function.
Answer/Conclusion
- The range exists from negative value which is -9 to the maximum value which is 5.
- That means the range is -9<=y<=5
