Let's look at the image of the function. The image of a linear function is a straight line, because the form of a linear function is y=kx+b, where k and b are constants. When k is a positive number, the straight line shows an upward trend; When k is negative, the straight line shows a downward trend. The value of b determines the intersection position of the straight line and the y axis.
We further analyze the properties of linear functions. The slope property of linear function is one of its core properties. The slope k reflects the steepness of the function image, and its value is equal to the ratio of vertical distance to horizontal distance of any two points on the function image. We also need to know the nature of the intercept b, which represents the intersection of the function and the Y axis, and its value has an important influence on the shape of the function.
Linear functions are also monotonous. When k is greater than 0, the function monotonically increases in the definition domain; When k is less than 0, the function monotonically decreases in the definition domain. This property is of great guiding significance for us to solve the problems related to monotonicity.
We also want to discuss the parity of functions. The images of odd-numbered functions and even-numbered functions are symmetrical, which is an important basis for us to solve problems related to symmetry. Through these properties, we can better understand and apply linear functions to solve practical problems.
Below the function image:
1, constant function: the image is a horizontal straight line, indicating that the values in the definition domain are all equal.
2. Linear function: The image is a straight line with two parameters: slope and intercept.
3. Quadratic function: the image is a parabolic curved mask with an upward or downward opening, and its shape is determined by quadratic coefficient A. ..
4. Cubic function: the image is an S-shaped curve, and the embedded function value increases or decreases with the increase or decrease of independent variables.
5. Exponential function: When bases are different, the images of the macro numbers of the exponential function are in the same coordinate system. Generally, you can make a straight line x= 1, and compare the intersection with each function according to the size of the ordinate of the intersection.
6. Logarithmic function: When the base is different, the image of logarithmic function is transformed like this.