Question

Which of the following is an example of a function
whose graph in the xy-plane has no x-intercepts?
A) A linear function whose rate of change is not
B) A quadratic function with real menos
© A quadratic function with no real xeros
D) A cubic polynomial with at least one real zero

Answer 1

Answer: Option C.

Step-by-step explanation:

A function goes trough the x-axis when f(x) = 0 for some value of x.

For example, when we say that a quadratic function has no real zeros, this means that the determinant is less than zero, so the roots of the equation:

a*x^2 + b*x + c = 0

are complex roots, this means that for the function:

f(x) = y = a*x^2 + b*x + c

there is not a real number x such f(x) = 0

So the correct option is C.

Answer 2

The quadratic function with no real zeros is an example of a function whose graph in the xy-plane has no x-intercepts.

What is x-intercept?

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis.

The example of a function whose graph in the xy-plane has no x-intercepts has to find out.
X-intercept is the point over the graph where,

$y=f(x)$

Here, x is the roots of the function.

For no value of x-intercepts, the function become,

$y=0$

$f(x)=0$

Here, the zeros and roots are the same, where function become equal to zero.

Thus, the quadratic function with no real zeros is an example of a function whose graph in the xy-plane has no x-intercepts.

Learn more about the x-intercept here;

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