Bolton Hobbs
09/05/2023 · Middle School
Given: \( f(x)=\frac{-3}{x+2}+1 \) and \( g(x)=2^{-x}-4 \) 5.1 Determine \( f(-3) \). 5.2 Determine \( x \) if \( g(x)=4 \). 5.3 Write down the asymptotes of \( f \) 5.4 .5 Drite down the range of \( g \). 6 Determine the coordinates of the \( x \) - and \( y \)-intercepts of \( f \). Determine the equation of the axis of symmetry of \( f \) which has a negative gradient. Leave your answer in the form \( y=m x+c \).
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5.1 \( f(-3) = 4 \).
5.2 \( x = -3 \).
5.3 Vertical asymptote: \( x = -2 \), Horizontal asymptote: \( y = 1 \).
5.4 Range of \( g \): \( (-4, \infty) \).
6. \( x \)-intercept: \( (1, 0) \), \( y \)-intercept: \( (0, -\frac{1}{2}) \).
The axis of symmetry for \( f \) is not in the form \( y = mx + c \), but it can be represented by the horizontal line \( y = -\frac{1}{2} \).
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