Examine the graphs and match each one with the correct coordinate rotation. You should match one graph with one rule.
1 answer:
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Answer:
The third sequence.
Step-by-step explanation:
In an arithmetic sequence, the difference between two consecutive terms is the same.
For each option, find the difference between consecutive terms:
First option:
.
.
.
The differences are not the same. As a result, this option is not an arithmetic sequence.
Second option:
.
.
.
The differences are not the same. As a result, this option is not an arithmetic sequence, either.
Third option:
.
.
.
The differences are all . As a result, this option is indeed an arithmetic sequence. Its common difference is
.
Fourth option:
.
.
The differences are varying between and
. As a result, this option is not an arithmetic sequence.
Step-by-step explanation:
The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as
.
This definition of the absolute function can be explained geometrically to be similar to the straight line , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line
where
(shown as the orange dotted line), the segment of the line is reflected across the <em>x</em>-axis.
First, we simplify the expression.
.
We, now, can simply visualise the straight line, , as a line having its y-intercept at the point
and its <em>x</em>-intercept at the point
. Then, imagine that the segment of the line where
to be reflected along the <em>x</em>-axis, and you get the graph of the absolute function
.
Consider the inequality
,
this statement can actually be conceptualise as the question
.
Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).
- Case 1 (when
)
- Case 2 (when
)
*remember to flip the inequality sign when multiplying or dividing by
negative numbers on both sides of the statement.
Therefore, the values of <em>x</em> that satisfy this inequality lie within the interval
.
Similarly, on the real number line, the interval is shown below.
The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.
