The graph of the function f(x) = (x − 3)(x + 1) is shown.
2 answers:
Answer:
Real values of x where x < -1
Step-by-step explanation:
Above the x-axis, the function is positive.
The function is decreasing when the gradient is negative.
The function has a positive
coefficient, therefore the vertex is a local minimum;
This means the gradients are negative before the vertex and positive after it;
To meet the conditions therefore, the function must be before the vertex and above the x-axis;
This will be anywhere before the x-intercept at x = -1;
Hence it is when x < -1.
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Given:
The pair of expressions in the options.
To find:
The two expressions are equivalent for any value of y.
Solution:
Two expressions are equivalent for any value of y, iff they are equivalent.
Clearly, is not equivalent to
or
. So, options A and B are incorrect.
The expression is not equivalent to
. So, option C is incorrect.
The expression is equivalent to
.
Therefore, the correct option is D.