Mathematics 1 Dersi 3. Ünite Sorularla Öğrenelim

What is a polynomial function with degree 1 called?

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

What is a polynomial function with degree 2 called?

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

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

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.

What is a polynomial equation?

If f (x)=0 then its called a polynomial equation. Therefore the polynomial equations are equations of the form
a_nxⁿ+a_n-1x^n-1+...+a₂x²+a₁x+a₀=0

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

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

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

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

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

The solution set is {–b/a}

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

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}.

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

This equation is called a quadratic equation in one variable.

What are the identities?

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

What is the discriminant of the quadratic equation?

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.

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

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.

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

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.

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

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

What are horizontal lines? 

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.

What is a vertical line?

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

When are two lines  parallel to eachother?

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.

What is a parabola?

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. 

What is the vertex of the parabola?

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).

What is a linear inequality?

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.

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

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

What is a quadratic inequality?

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.