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Mathematics 1 Dersi 3. Ünite Sorularla Öğrenelim

Polynomial Functions

1. Soru

What is a polynomial function with degree 1 called?

Cevap

A polynomial function with degree 1 is called a linear function.


2. Soru

What is a polynomial function with degree 2 called?

Cevap

A polynomial function with degree 2 is called a quadratic function.


3. Soru

Why cannot this function (f(x) =x2 - 1/x) be polynomial function ?

Cevap

This is a function but not a polynomial. The term 1/x is equal to x-1. Since –1 is not a natural number, the function cannot be a polynomial function.


4. Soru

What is a polynomial equation?

Cevap

If f (x)=0 then its called a polynomial equation. Therefore the polynomial equations are equations of the form
anxn+an-1xn-1+...+a2x2+a1x+a0=0


5. Soru

Is 2x7– x3+1=0 this equation polynomial?

Cevap

A polynomial equation is also called an algebraic equation, so this is a polynomial equation.


6. Soru

When f (x)= ax+b=0 and a and b are real numbers and a?0, what is this equation called?

Cevap

where a and b are real numbers and a?0. This equation is called a linear equation in one variable.


7. Soru

What is the solution set of the root of the linear function of ax+b=0(a?0)?

Cevap

The solution set is {–b/a}


8. Soru

Find the solution of the linear equation
5(x+1) – 3(x+1) = 4.

Cevap

5x+5–3x–3=4 Using distribution property

2x+2=4 Re-write equation.

2x=2

x=1

So, x=1 is the solution of the equation. The solution set is denoted as {1}.


9. Soru

What is the equation called when  f (x) = ax2+bx+c=0 where a, b and c are real numbers and a?0?

Cevap

This equation is called a quadratic equation in one variable.


10. Soru

What are the identities?

Cevap

(x+y)2= x2+2xy+y2
(x–y)2= x2–2xy + y2
These identities are frequently used in obtaining the solutions of quadratic equations.


11. Soru

What is the discriminant of the quadratic equation?

Cevap

In the quadratic formula, b2–4ac is called the discriminant of the quadratic equation and we use
the symbol ? (capital Greek delta) for discriminant:
?= b2–4ac
If the discriminant is positive, then there are two distinct roots.If the discriminant is zero, then there is exactly one real root. If the discriminant is negative, then there are no real roots.


12. Soru

How many dimensions does the graph of a function f have?

Cevap

The graph of a function f is the collection of all ordered pairs. The graph is drawn on the Cartesian coordinate system. So, the graph has two dimensions.


13. Soru

What are  x-intercept and y-intercept on the graph of f?

Cevap

An x-intercept is a point on the graph of f where y is zero and a y -intercept is a point on the graph of f where x is zero.


14. Soru

What is the slope of the line through the points (x1, y1) and (x2, y2)?

Cevap

Mathematics has developed a useful measure for the steepness of a line, called the slope of
the line. The slope of the line through the points (x1, y1) and (x2, y2) is
slope =Change in y/Change in x = (y2 - y1) /(x2 - x1) where x1?x2


15. Soru

What are horizontal lines? 

Cevap

Some lines may have slope 0. Such lines have the form y=b, and are called horizontal lines.    y=–1, y=2, etc. are examples of such lines. Horizontal lines are parallel to the x-axis.


16. Soru

What is a vertical line?

Cevap

If the line is parallel to y-axis then, it is in the form x=c and is called a vertical line.


17. Soru

When are two lines  parallel to eachother?

Cevap

Two lines are parallel if and only if their slopes are the same. For example, the lines y=3x–2 and
y=3x have the same slope.


18. Soru

What is a parabola?

Cevap

Let f (x)= ax2+bx+c, a?0 be a quadratic function. The graph of f (x) is called a parabola. In what
follows we use f (x) = y (i.e. y= ax2+bx+c). Parabolas have shapes similar to a soup bowl.If the leading coefficient is positive, the parabola opens upward. If the leading coefficient is negative, the parabola opens downward. 


19. Soru

What is the vertex of the parabola?

Cevap

The vertex of the parabola is the lowest point on the graph if the graph opens upward, and the
highest point on the graph if it opens downward. The parabola is a symmetric figure and the axis
of symmetry is x=h where the vertex is (h, k).


20. Soru

What is a linear inequality?

Cevap

We already know that any equation of the form y=ax+b where a?0, is a linear equation. Any of the following inequalities y>0, y?0, y<0 and y?0, is called a linear inequality.


21. Soru

What should be done when the inequality is multiplied or divided by a negative number?

Cevap

Do not forget that the inequality symbol is reversed when the inequality is multiplied or
divided by a negative number.


22. Soru

What is a quadratic inequality?

Cevap

For a?0, y= ax2+bx+c defines a quadratic equation. Any of the following inequalities y>0, y<0, y?0, and y?0 is called a quadratic inequality.


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