A function assigns the values. The statements that are true about the given function are B and D.
A function assigns the value of each element of one set to the other specific element of another set.
To know the correct statements about the graph of the function f(x)=6x-4+x², we need to plot the graph, as shown below.
A.) The vertex form of the function is f(x)=(x-2)²+2.
To know if the vertex form of the function is f(x)=(x-2)²+2, solve the equation and check if it is of the form f(x)=6x-4+x².
[tex]f(x)=(x-2)^2+2\\\\ f(x)=x^2+4-4x+2\\\\f(x) = x^2-4x+6[/tex]
Since the two functions are not equal this is not the vertex form of the function is f(x)=6x-4+x².
B.) The vertex of the function is (-3, -13).
As can be seen in the image below, the vertex of the function lies at (-3,-13.) Therefore, the statement is true.
C.) The axis of symmetry for the function is x = 3.
As the vertex is at -3, therefore, the function symmetry will be about x=-3.
Hence, the given statement is false.
D.) The graph increases over the interval (-3).
The given statement is true since the graph will be showing a positive slope in the interval (-3, +∞).
E.) The function does not cross the x-axis.
It can be observed that the function intersects the x-axis exactly at two points, therefore, the given statement is false.
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