How can the graph of g(x)=3square root x+3 be obtained from the graph of g(x)= 3 square root x?
A. shift the graph 3 units right
b. shift the graph 3 units up
c. shift the graph 3 units down
d. shift the graph 3 units left
I am having problems with the square roots. Can someone please help!!
To understand how the graph of g(x)=3√x+3 can be obtained from the graph of g(x)=3√x, let's first understand the effect of each transformation.
The original function g(x)=3√x represents the square root of x, multiplied by 3, which stretches the graph vertically by a factor of 3. The graph starts from the point (0,0), and as the x-values increase, the y-values increase at a slower rate due to the square root function.
Now, let's consider the new function g(x)=3√x+3. The "+3" in the equation indicates a vertical shift of the entire graph. To understand which direction the shift occurs, we need to think about what happens to the y-values.
When x=0, y=3 in the new equation. This means that at x=0, the y-value is increased by 3 units compared to the original graph. Therefore, the correct answer is (b) shift the graph 3 units up.
In summary, to obtain the graph of g(x)=3√x+3 from g(x)=3√x, you need to stretch the graph vertically by a factor of 3 and then shift it upwards by 3 units.