The graph for the linear function, g(x) = -x + 1 is shown in the image attached below.
What is a Linear Function?
If m represents the slope and b represents the y-intercept of a function, the equation that represents the linear function would be expressed as, y = mx + b
Slope (m) = rise/run = change in y/change in x.
Find the equation of function f:
Slope (m) of function f = rise/run = 2/1
Slope (m) = 2
y-intercept, b, for function f = the point on the y-axis that the line intercepts = -6.
Write the equation for function f by substituting m = 2 and b = -6 into f(x) = mx + b.
f(x) = 2x + (-6)
f(x) = 2x - 6
Given that, g(x) = -½f(x + 2), therefore:
g(x) = -½(2(x + 2) - 6)
g(x) = -½(2x + 4 - 6)
g(x) = -½(2x - 2)
g(x) = -x + 1
Thus, the graph for the linear function, g(x) = -x + 1 is shown in the image attached below.
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