Question

Провести повне дослідження функції та побудувати її графік : 1)y= x^2-6x+4 / 3x-2 2)р=кореньSin a пожалуйста помогите :(

Answer 1

1 задача

 

 

 

 

 

 

 

 

 

2 задача

 

 

 

 нужны только графики???

 

Answer 2

Function Analysis and Graph Plotting

1) The given function is y = (x^2 - 6x + 4) / (3x - 2).

To analyze the function and plot its graph, we can follow these steps:

Step 1: Determine the domain of the function. The function is defined for all real numbers except when the denominator is equal to zero. So, we need to find the values of x that make the denominator zero and exclude them from the domain. In this case, the denominator is 3x - 2, so we set it equal to zero and solve for x: 3x - 2 = 0 3x = 2 x = 2/3

Therefore, the domain of the function is all real numbers except x = 2/3.

Step 2: Determine the vertical asymptotes. Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. In this case, the vertical asymptote occurs when the denominator is zero, which is x = 2/3.

Step 3: Determine the x-intercepts. To find the x-intercepts, we set y = 0 and solve for x: x^2 - 6x + 4 = 0

Using the quadratic formula, we can find the solutions for x: x = (-(-6) ± √((-6)^2 - 4(1)(4))) / (2(1)) x = (6 ± √(36 - 16)) / 2 x = (6 ± √20) / 2 x = (6 ± 2√5) / 2 x = 3 ± √5

Therefore, the x-intercepts are x = 3 + √5 and x = 3 - √5.

Step 4: Determine the y-intercept. To find the y-intercept, we set x = 0 and solve for y: y = (0^2 - 6(0) + 4) / (3(0) - 2) y = 4 / (-2) y = -2

Therefore, the y-intercept is y = -2.

Step 5: Determine the behavior of the function as x approaches positive and negative infinity. As x approaches positive infinity, the leading term in the numerator (x^2) dominates, and the function approaches positive infinity. As x approaches negative infinity, the leading term in the numerator (x^2) dominates, and the function approaches positive infinity.

Step 6: Plot the graph. Using the information obtained from the previous steps, we can plot the graph of the function. Here is the graph:


2) The given equation is p = sqrt(sin(a)).

To analyze the equation, we can follow these steps:

Step 1: Determine the domain of the equation. The square root function is defined for non-negative real numbers. Therefore, the domain of the equation is all real numbers.

Step 2: Plot the graph. Since the equation involves only one variable, we can directly plot the graph of p as a function of a. Here is the graph:


Please note that the graphs provided above are for illustrative purposes only and may not be accurate representations of the actual graphs. It is always recommended to use graphing software or calculators to obtain precise graphs.