Answer:
The function f(x) intercepts the x-axis at (0,0), thus it touches the x-axis once.The graph of the function g(x) does not intercept the x-axis at all.
Explanation:
In this question you first form the table for values of x with corresponding values of f(x) that you will use to graph the function f(x)=x².Then do the same for the function g(x)=x²+2.Take a point from the parent function f(x) and compare it with its image in the function g(x) to identify the transformation that occurred.Graph the two equations to visually see the x-intercepts in both equations.
In the parent function f(x)=x² form a table as shown below;
x f(x)=x² coordinate to plot
-3 -3²=9 (-3,9)
-2 -2²=4 (-2,4)
-1 -1²=1 (-1,1)
0 0²=0 (0,0)
1 1²=1 (1,1)
2 2²=4 (2,4)
3 3²=9 (3,9)
Use the coordinates to plot the graph of f(x)=x² on a graph tool and see the number of x-intercept values
In the function g(x)=x²+2 also form your table for values of g(x) with corresponding values of x
x g(x)=x²+2 coordinate to plot
-3 -3²+2=9+2=11 (-3,11)
-2 -2²+2=4+2=6 (-2,6)
-1 -1²+2=1+2=3 (-1,3)
0 0²+2=2 (0,2)
1 1²+2=1+2=3 (1,3)
2 2²+2=4+2=6 (2,6)
3 3²+2=9+2=11 (3,11)
Use the coordinates to plot the graph of g(x)=x²+2 on a graph tool to determine the number of x intercept values
You can determine the transformation that occurred too, how?
Take a point on the parent function f(x) and compare it with its image in the function g(x)
Let take point (-3,9) and compare it to (-3,11).You notice x coordinate did not change but the y coordinate shifted 2 units upwards along the y-axis.To determine this dilation you subtract the coordinates of object point from that of image point.
The dilation was (0,2)
Solution
From the graphs, the function f(x), intercepts the x-axis at (0,0), thus it touches the x-axis once.The graph of the function g(x) does not intercept the x-axis at all.