on the provided graph, plot the points where the following function crosses the x - axis and the y…
on the provided graph, plot the points where the following function crosses the x - axis and the y - axis.\ng(x)=-5^{x}+5
Answer
Explanation:
Step1: Find the y - intercept
The y - intercept occurs when (x = 0). Substitute (x = 0) into (g(x)=-5^{x}+5): (g(0)=-5^{0}+5) Since (a^{0}=1(a\neq0)), then (g(0)=-1 + 5=4). So the y - intercept is the point ((0,4)).
Step2: Find the x - intercept
The x - intercept occurs when (y = g(x)=0). Set (-5^{x}+5 = 0). Add (5^{x}) to both sides: (5=5^{x}). Since (y = a^{x}) ((a>0,a\neq1)) and when (a = 5), if (5^{1}=5), then (x = 1). So the x - intercept is the point ((1,0)).
Answer:
The function (g(x)=-5^{x}+5) crosses the y - axis at ((0,4)) and the x - axis at ((1,0)).