Learn to translate an exponential graph using a reflection and horizontal shift

The video tutorial explains how to graph the equation Y = -2^(X+2) by first graphing Y = 2^X, identifying transformations such as reflection over the X-axis, and applying horizontal shifts. The process involves using a table of values and understanding the impact of negative signs and shifts within the function. The final graph is a reflection and shift of the base graph.

What is the first step when graphing an equation like y = -2^x + 2?

• Add 2 to the y-values

• Reflect over the x-axis

• Shift the graph 2 units left

• Graph y = 2^x

What is the significance of the point (0,1) in the base graph y = 2^x?

• It is the x-intercept of the graph

• It is the y-intercept of the graph

• It is the vertex of the graph

• It is a point of reflection

How does the negative sign in y = -2^x affect the graph?

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

• It shifts the graph upwards

• It shifts the graph downwards

What transformation is applied when the equation includes x + 2 inside the function?

• Shift 2 units to the right

• Shift 2 units to the left

• Shift 2 units upwards

• Shift 2 units downwards

After applying all transformations, what is the final step in graphing the equation?

• Plot the final graph

• Check for symmetry

• Add more points

• Erase the base graph