Junior high school mathematics knowledge point induction (formula)-function

Discrimination of positive proportional function

To judge the proportional function, the test is divided into two steps.

One quantity means another quantity, right?

Look at the numerical values, all you need is real numbers.

Distinguishing the proportional function, the measurement can be divided into two steps.

One quantity means another quantity, right or wrong.

If there is, it depends on the value. All real numbers must be there.

Images and properties of proportional function

Line, passage and origin of proportional function graph.

K is positive one, three, negative two and four, and the changing trend is in the heart.

K is low on the left and high on the right, climbing in the same direction.

K is negative, the left is high and the right is low, and the mountain is one big and one small.

linear function

Linear function diagram straight line, passing point.

K is low on the left and high on the right, and the higher you climb, the higher you climb.

K is negative, higher left and lower right, and lower and lower.

K is called the slope b intercept, and the zero intercept becomes a positive function.

inverse proportion function

Inverse hyperbola, crossing point.

K is plus one, three, minus two, four, and the two axes are its asymptotes.

K is high on the left and low on the right, and one or three quadrants slide down the mountain.

K is negative, low left and high right, and the second and fourth quadrants are like climbing mountains.

quadratic function

When the quadratic equation changes from zero to y, a quadratic function appears.

All real numbers define the domain, and images are called parabolas.

A parabola has an axis of symmetry, and both sides are monotonous and opposite.

A determines the opening and size, and the intersection of spools is called the vertex.

Vertex is either high or low. Up and down are conspicuous.

If you want to draw a parabola, you can also translate the pursuit point.

Extract formulas and set vertices, and then select them in two ways.

After drawing the list, connect the lines and keep the translation rules in mind.

Add parentheses to the left and right, and add and subtract redundant numbers.

For y, you get a quadratic function.

The image is called parabola, which defines all the real numbers in the domain.

A set the opening and size, with the opening facing upward.

The absolute value is large and the opening is small, and the opening is negative.

Parabola has an axis of symmetry, and the increase and decrease characteristics can be seen in the figure.

The intersection of axes is called the vertex, and the ordinate of the vertex is the most valuable.

If you want to draw a parabola, trace the point and translate two roads.

Select the fixed vertex of the formula and draw all translation points.

After the list is drawn, connect the lines, and three points roughly define the whole picture.

If you want to translate, it is not difficult to draw a basic parabola first

The vertex moves to the new position, and the size of the opening follows the foundation.