Graph and compare the shapes and key features of the functions f(x)=(x+2)2 and g(x)=2x+4 (5 points) The function f(x)= (x+2)2 is while the function g(x)=2x+4 is . They have domain which is . The two graphs have range, which is . They have the x-intercept, which is . Both graph have the y-intercept which is
The function f(x) = (x+2)^2 is a quadratic function that opens upwards. It forms a U-shaped curve known as a parabola. The key feature of this function is that it has a vertex at (-2, 0). The vertex is the lowest point of the parabola.
The function g(x) = 2x +4 is a linear function that represents a straight line on the graph. It has a constant rate of change and does not curve like a parabola. The key feature of this function is that it has a y-intercept at (0, 4). This means that when x=0, the y-coordinate is 4.
The domain of both functions is all real numbers since there are no restrictions on the x-values.
The range of f(x) depends on the vertex. In this case, since the vertex is at (−2, 0), the range is greater than or equal to 0. In other words, f(x) is always greater than or equal to zero.
The range of g(x) is all real numbers since the line extends infinitely in both the positive and negative y-directions.
Both functions have an x-intercept at (-2, 0) because f(x) = 0 when x = -2. Thus, the x-coordinate of the vertex is also the x-intercept.
Both functions have a y-intercept at (0, 4) because g(0) = 2(0) + 4 = 4. Thus, the value of y when x=0 is 4 for both functions.