Use your graph to determine the value(s) of $x$ for which:
5.4.1 $f(x) \times g(x) > 0$
5.4.2 $g(x) < -1$ - NSC Mathematics - Question 7 - 2019 - Paper 1
Question 7
Use your graph to determine the value(s) of $x$ for which:
5.4.1 $f(x) \times g(x) > 0$
5.4.2 $g(x) < -1$
Worked Solution & Example Answer:Use your graph to determine the value(s) of $x$ for which:
5.4.1 $f(x) \times g(x) > 0$
5.4.2 $g(x) < -1$ - NSC Mathematics - Question 7 - 2019 - Paper 1
Step 1
5.4.1 $f(x) \times g(x) > 0$
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Answer
To find where the product of f(x) and g(x) is greater than 0, we need to examine the signs of both functions.
Identify regions on the graph where both f(x) and g(x) are positive.
Identify regions where both functions are negative.
Note the intervals where the product f(x)×g(x)>0, which will be the union of those two regions.
Step 2
5.4.2 $g(x) < -1$
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Answer
To determine where g(x)<−1, follow these steps:
Locate the horizontal line y=−1 on your graph of g(x).
Identify the intervals where the graph of g(x) is positioned below this line.
The x-coordinates corresponding to these intervals will provide the solutions for the inequality.
