The statement, the function f(x) =a^x-4 will never cross the x-axis if a is positive is a false statement.
What is a function?
A function can then be defined as a set of ordered pairs. Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
For the given situation,
The function is f(x) =a^x-4
Let us assume a positive number, a=2
⇒ [tex]f(x)=2^{x}-4[/tex]
Plot this function in the graph as shown.
From the graph it is clearly seen that the function crosses the x-axis.
Hence we can conclude that the statement, the function f(x) =a^x-4 will never cross the x-axis if a is positive is a false statement.
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