Point at which they intersect is going to have a single y value and a single x value. So at that point, the x and y values are equal:
![y=x^{2}-3 \\ y=3x-4 \\ x^{2}-3=3x-4 \\ x^{2}-3x+1=0 \\ x= \frac{-b± \sqrt{b^{2}-4ac} }{2a} \\ x= \frac{3± \sqrt{9-4} }{2} \\ x= \frac{3± \sqrt{5} }{2} \\ x=2.62, 0.38 ](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D-3%20%5C%5C%0Ay%3D3x-4%20%5C%5C%0Ax%5E%7B2%7D-3%3D3x-4%20%5C%5C%20%0Ax%5E%7B2%7D-3x%2B1%3D0%20%5C%5C%20%0Ax%3D%20%5Cfrac%7B-b%C2%B1%20%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%20%7D%7B2a%7D%20%5C%5C%20%0Ax%3D%20%5Cfrac%7B3%C2%B1%20%5Csqrt%7B9-4%7D%20%7D%7B2%7D%20%5C%5C%20%0Ax%3D%20%5Cfrac%7B3%C2%B1%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20%5C%5C%20%0Ax%3D2.62%2C%200.38%0A)
So the lines intersect at two x values, 2.62 and 0.38. Now plug them into either equation to find the y values:
![y=3(2.62)-4 \\ y=3.86](https://tex.z-dn.net/?f=y%3D3%282.62%29-4%20%5C%5C%0Ay%3D3.86%20)
![y=3(0.38)-4 \\ y=-2.86](https://tex.z-dn.net/?f=y%3D3%280.38%29-4%20%5C%5C%20%0Ay%3D-2.86)
So the lines intersect at (2.62,3.86) and (0.38,-2.86)
Answer:
x=2?
Step-by-step explanation:
Answer:
Option (d).
Step-by-step explanation:
Note: The base of log is missing in h(x).
Consider the given functions are
The function m(x) can be written as
...(1)
The translation is defined as
.... (2)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
![a=3,b=0](https://tex.z-dn.net/?f=a%3D3%2Cb%3D0)
Therefore, we have to translate each point of the graph of h(x) 3 units left to get the graph of m(x).
Hence, option (d) is correct.